In the realm of philosophy of religion, I'm acquainted with concepts like divine hiddenness and the idea of a non-resistant non-believer, which refers to someone open to, yet lacking, a genuinely meaningful and reciprocal conscious connection with God (as explained by the author of this answer). From a Christian viewpoint, if a person (non-believer or otherwise) is (or claims to be) open to God and yet consistently reports an inability to experience or establish a spiritual connection or relationship with Him—a state commonly described as God being perceived as hidden—over a span of many years, perhaps even a lifetime (as seen in individuals self-identifying as life-long non-resistant non-believers), is there a specific term in Christianity that best captures the condition of such a person?
After a cursory investigation, I found the following related terms:
Spiritual dryness or desolation:
In Catholic spirituality, spiritual dryness or desolation is a lack of spiritual consolation in one's spiritual life. It is a form of spiritual crisis experienced subjectively as a sense of separation from God or lack of spiritual feeling, especially during contemplative prayer. It is thought that spiritual dryness can lead to greater love of God.
(Source Wikipedia: Spiritual dryness)
Dark Night of the Soul:
The Dark Night of the Soul (La noche oscura del alma) is a phase of passive purification of the spirit in the mystical development, as described by the 16th-century Spanish mystic and poet St. John of the Cross in his treatise Dark Night (Noche Oscura), a commentary on his poem with the same name. It follows after the second phase, the illumination in which God's presence is felt, but this presence is not yet stable. The author himself did not give any title to his poem, which together with this commentary and the Ascent of Mount Carmel (Subida del Monte Carmelo) forms a treatise on the active and passive purification of the senses and the spirit, leading to mystical union.
In modern times, the phrase "dark night of the soul" is used to describe a crisis of faith or a difficult, painful period in one's life.
(Source Wikipedia: Dark Night of the Soul)
To be spiritually blind is not to see Christ, and not to see Christ is not to see God (Colossians 1:15-16; 2 Corinthians 4:6). Spiritual blindness is a grievous condition experienced by those who do not believe in God, Jesus Christ, and His Word (Romans 2:8; 2 Thessalonians 2:12). Those who reject Christ are the lost (John 6:68-69). Being spiritually blind, they are perishing (2 Corinthians 4:3-4; Revelation 3:17). They choose not to accept the teachings of Christ and His authority in their lives (Matthew 28:18). They are blind to the manifestations of God as revealed throughout His Word and Jesus Christ (John 1:1; Acts 28:26-27). They are described as those who “do not accept the things of the Spirit of God, for they are folly to him, and he is not able to understand them because they are spiritually discerned” (1 Corinthians 2:14).
(Source What is spiritual blindness?)
Of these three, spiritual blindness seems to be the most fitting for a person who self-identifies as non-resistant non-believer. The non-resistant non-believer would thus need to figure out a plan to overcome their own spiritual blindness, in order to be able to perceive the divine presence, leaving behind the previous state of apparent divine hiddenness.
Is there a Christian term for the condition of a person who is unable to experience a spiritual connection with God?
Going out on a limb here and going to speculate that the only term that would truly fit into this scenario would seem to be the term damned. It would seem most becoming that this term would the only one that fit this because the the souls in hell, typically called the damned are deprived the presence of God!
Although some individuals may seemingly not feel the presence of God in their life while here on earth, this is in reality untrue. God is present in our lives, whether we feel his presence in this life or not.
This being stated, such terms as spiritual dryness or desolation, dark night of the soul and spiritual blindness are terms that generally used to explain spiritual dryness in regards to faith in God. In Catholic theology, the dark night of the soul is looked on as a form of spiritual form of purification or trial in order to achieve a more complete spiritual and mystical union with God.
Mystical theology is the branch of theology in the Christian tradition that explains mystical practices and states, as induced by contemplative practices such as contemplative prayer, called theoria from the Greek for contemplation.
According to Saint Gregory the Great there are people by whom, "while still living in this corruptible flesh, yet growing in incalculable power by a certain piercingness of contemplation, the Eternal Brightness is able to be seen."
While the direct vision of God (the Beatific Vision) can be reached only in the next life, God does give to some a very special grace, by which he becomes intimately present to the created mind even before death, enabling it to contemplate him with ineffable joy and be mystically united with him even while still alive, true mystical contemplation. Saint Augustine said that, in contemplation, man meets God face-to-face.
Again, according to Catholic theology, things like desolation may happen to souls at any stage of their three spiritual development of States or Ways (Purgative, Illuminative, Unitive) in its quest for union with God.
Spiritual desolation means the feeling of abandonment by God, and of the absence of His grace. This feeling of estrangement may arise from various causes. It may be the result of natural disposition or temperament, or of external circumstances; or it may come from the attacks of the devil; or from God Himself when for our greater good He withdraws from us spiritual consolation. In contradistinction to consolation spiritual desolation may be of three kinds.
The first is called sensible desolation and is the opposite of sensible consolation. It includes aridities, dissipation of mind, weariness, and disgust in the exercises of piety; and it is often experienced by beginners in the practice of mental prayer. It may co-exist with consolation of a higher order just as, in the natural. order, we may pain of body and joy of soul at one and the same time.
The second kind of desolation affects the intellect and will, and consists in the privation of the feeling of the presence of the supernatural virtues as described by St. Teresa in her Life (ch. xxx). This trial is extremely severe, but if generously accepted, and patiently endured, it may be turned into great merit, and many fruits of sanctity will be the result. (See letter of St. Francis of Sales to S. Jane Frances de Chantal, 28 March, 1612).
The third kind of desolation is still more severe. It is a darkening of the mind and a feeling of abandonment so great that the soul is tempted to distrust concerning salvation and is tormented by other terrible thoughts against faith, against purity, and even by blasphemous thoughts--the most painful experience which a holy soul has to endure (see St. John of the Cross, op. cit., infra, bk. I, ch. xiv). It would be a great mistake to imagine that spiritual desolation arrests progress in virtue or enfeebles the spirit of fervour. On the contrary, it affords occasion of heroic virtue and of absolute detachment from sensible pleasure, whether natural or supernatural. At the same time we may hope and wish that these interior griefs may be diminished or made to disappear, and we may pray God to deliver us from them, but if all our efforts are in vain, and God permits the desolation to continue, it only remains to resign ourselves generously to His Divine Will.
In conclusion, I would like to share a prayer for obtaining the presence of God at all times.
God, my Father, You have promised to remain forever with those who do what is just and right. Help me to live in Your presence. The loving plan of Your Wisdom was made known when Jesus, your Son, became man like us. I want to obey His commandment of love and bring Your peace and joy to others. Keep before me the wisdom and love You have made known in Your Son. Help me to be like Him in word and deed. [Amen.]
Is there a Christian term for the condition of a person who subjectively feels incapable of experiencing a spiritual connection with God?
Confused and in need of a spiritual director or confesssor.
I'll offer some additional terminology from a Latter-day Saint perspective.
"Past feeling" is a term used twice in the Book of Mormon to describe people who could not perceive the influence of the Holy Ghost (1 Nephi 17:45, Moroni 9:20). In both cases the people described had made numerous life choices without concern for the commands of the Lord, and it left them in a place where their spiritual sensitivity was minimal (the analogy of eating a habanero pepper and then wondering why one can't taste anything for a while comes to mind).
The latter passage includes this illuminating comment:
thou knowest that they are without principle, and past feeling (excerpt from Moroni 9:20)
These individuals had no immovable moral foundation, no consistent guiding moral principles--this lack of an anchor in their lives left them easily susceptible to following the crowd wherever it went (and in the case of Moroni chapter 9, it went some pretty terrible places)
In both cases, the prescription to cure this ailment was very straightforward: repentance.
Veil/cloud of darkness
Another 2 examples from the Book of Mormon describe people as having a "dark veil of unbelief" or a "cloud of darkness" over them (Alma 19:6, Helaman 5:40-41).
In both cases it was necessary to replace darkness with light. When Lamoni (1st example) recognized the dark place he was in and that there were people he knew who had something different...something he needed...he prioritized it above everything else (see Alma 18:21).
In Aminadab's case (2nd example), the path forward was:
You must repent, and cry unto the voice, even until ye shall have faith in Christ, who was taught unto you by Alma, and Amulek, and Zeezrom; and when ye shall do this, the cloud of darkness shall be removed from overshadowing you. (excerpt from Helaman 5, see 5:21-50 for more complete context)
In both cases, replacing darkness with light required repentance.
Prisoner of doubt
Apostle Dieter F. Uchtdorf made the following (now famous in Latter-day Saint circles) statement in a sermon in 2013:
first doubt your doubts before you doubt your faith. We must never allow doubt to hold us prisoner and keep us from the divine love, peace, and gifts that come through faith in the Lord Jesus Christ. (source)
In addition to being solid spiritual guidance, the statement is philosophically profound. As I've written about here and here, and as demonstrated by many answers here, people have a remarkable tendency to hold others' views to a standard that they would never apply to their own views. Whether we are sufficiently self-aware to acknowledge it or not, we all believe something.
We cannot function in a space of total doubt; every action we take has a basis in some belief we hold. Doubt, on the other hand, is a weed that casts is seeds on everything it touches, that can never be satisfied. It is always possible to one-up a doubt by doubting the reason for the doubt. And so, to borrow an idea from Jeff Bezos, we frequently have to make decisions based on enough information, even knowing that we do not have all information. This principle appears to have served Bezos' businesses fairly well =).
"Past feeling", being under a "cloud of darkness", and a "prisoner of doubt" are terms which can describe someone struggling to feel a connection to God. In some cases, these states are self-inflicted, in others, it is merely a result of not knowing where to turn:
For there are many yet on the earth among all sects, parties, and denominations, who are blinded by the subtle craftiness of men, whereby they lie in wait to deceive, and who are only kept from the truth because they know not where to find it (Doctrine & Covenants 123:12)
Identifying those things which restrict our ability to perceive the Holy Ghost -- aka repentance -- and being willing to take steps of faith based on what we do know, offer liberation from the prison of doubt and a path from this place of darkness into light.