Does the Catholic Church explain why Jesus only appeared in short apparitions to his followers post-resurrection?
The answer is Yes. The Catholic Church stated that we need to embraced the Life of Jesus as a Mystery for us to meditate and contemplate as we journey along the Christian path. Therefore, the bible does not reveals every minute details of Christ works but only those important truth that will lead us to follow Jesus Christ.
The Logos was incarnated with a mission to Redeem & Resurrect all mankind and to dwell among us.
"The Word became flesh and made his dwelling among us. We have seen his glory, the glory of the one and only Son, who came from the Father, full of grace and truth.(John1:14)
The resurrection of Christ body was not a return to normal life but only to witness the fulfillment of His promised ressurection of the body to those who followed and put their faith in Him.
999 How? Christ is raised with his own body: "See my hands and my feet, that it is I myself";553 but he did not return to an earthly life. So, in him, "all of them will rise again with their own bodies which they now bear," but Christ "will change our lowly body to be like his glorious body," into a "spiritual body":554
Jesus did not return to earthly life to "dwell again" among us but to proclaim the fulfillment of His promised of Resurrection to all and for the Apostles and Disciples becomes a living witness to His Resurrection.
995 To be a witness to Christ is to be a "witness to his Resurrection," to "[have eaten and drunk] with him after he rose from the dead."549 Encounters with the risen Christ characterize the Christian hope of resurrection. We shall rise like Christ, with him, and through him.
This is only the purpose why Jesus had a short apparitions and had chosen to appear only a few occasions to all Apostles and Disciples who received the Gift of the Holy Spirit. The scriptures numbered the apparitions in ten occasions within the forty days period prior to His Ascension.
Let us remember that the Redemptive Works of Jesus Christ was already finished At the Foot of the Cross before He exhaled His last breath.
John 19:28-30 New King James Version (NKJV)
It Is Finished
28 After this, Jesus, [a]knowing that all things were now accomplished, that the Scripture might be fulfilled, said, “I thirst!” 29 Now a vessel full of sour wine was sitting there; and they filled a sponge with sour wine, put it on hyssop, and put it to His mouth. 30 So when Jesus had received the sour wine, He said, “It is finished!” And bowing His head, He gave up His spirit.
In closing, the Gospel and the Book of Acts of the Apostles only mentioned a short apparitions as Jesus resurrected life was not a return to normal earthly life but simply Jesus witnessing to the power of His words promising Eternal Life.
"I am the Resurrection and the life."(John11:25)
Additional answer from Catechism of the Catholic Church:
Catholic Church teaches to view the Life of Christ as a Mystery when the scriptures is silent, and to follow the path of the Saints who contemplate the Mystery of Christ Life thru the eyes of His Mother the Theotokos.
I. CHRIST'S WHOLE LIFE IS MYSTERY
514 Many things about Jesus of interest to human curiosity do not figure in the Gospels. Almost nothing is said about his hidden life at Nazareth, and even a great part of his public life is not recounted.172 What is written in the Gospels was set down there "so that you may believe that Jesus is the Christ, the Son of God, and that believing you may have life in his name."173
515 The Gospels were written by men who were among the first to have the faith174 and wanted to share it with others. Having known in faith who Jesus is, they could see and make others see the traces of his mystery in all his earthly life. From the swaddling clothes of his birth to the vinegar of his Passion and the shroud of his Resurrection, everything in Jesus' life was a sign of his mystery.175 His deeds, miracles and words all revealed that "in him the whole fullness of deity dwells bodily."176 His humanity appeared as "sacrament", that is, the sign and instrument, of his divinity and of the salvation he brings: what was visible in his earthly life leads to the invisible mystery of his divine sonship and redemptive mission
For you other questions; "The Gospels give the account of ten apparitions of Jesus, which he allowed his followers after the resurrection.The longest time he spent with them was perhaps during the co-journey to Emmaus, that too, in disguise. Given that he spent forty days on earth between his resurrection and ascension, also given that he had 'descended into hell and preached' between the time of his death and resurrection, one is eager to know why Jesus did not spend much time with his disciples during the forty days prior to ascension."
Don't forget that Jesus uses numbers to convey a deeper meaning to the Jews as they speak the Hebrew language. The number ten and forty has meaning in Church Tradition.
What Does The Number Ten (10) Mean or Represent in the Bible?
How about the meaning of forty days in Catholic Tradition?
Catholic Activity: Why Forty Days?
Lastly your final question is; "My question, therefore, is: How does the Catholic Church explain the absence of longer periods of Jesus's stay with his followers post-resurrection?"
The Catechism of the Catholic Church acknowledge the Life of Christ as a Mystery and be found in details here;
Paragraph 3. The Mysteries of Christ's Life
512 Concerning Christ's life the Creed speaks only about the mysteries of the Incarnation (conception and birth) and Paschal mystery (passion, crucifixion, death, burial, descent into hell, resurrection and ascension). It says nothing explicitly about the mysteries of Jesus' hidden or public life, but the articles of faith concerning his Incarnation and Passover do shed light on the whole of his earthly life. "All that Jesus did and taught, from the beginning until the day when he was taken up to heaven",171 is to be seen in the light of the mysteries of Christmas and Easter.
The Gospel of John had numerous passages that gave us passages to meditate and contemplate for us to understand the deeper things of God not reveals in the bible.
But, how do we know the deeper things about God especially Jesus mysterious life and works not written in the bible? We need to seek Wisdom that God said He will give generously to all who ask of it.
James 1:5 New International Version (NIV)
5 If any of you lacks wisdom, you should ask God, who gives generously to all without finding fault, and it will be given to you.
Why seek wisdom?
Wisdom is supreme; therefore acquire wisdom. And whatever else you obtain, gain understanding. (Proverbs4:7)
"Blessed are those who find wisdom, those who gain understanding,"(Proverbs3:13)
So, the answer to your question that entails a mystery is to seek Wisdom and King Solomon passages in Book of Wisdom is a good source as well as the Book of Proverbs. But as Catholic we have a short-cut to know the Mystery about Christ Life especially the hidden wisdom that was concealed by God purposely.
How does a Catholic faithful know the mystery of Christ? We seek the Wisdom who is a Mother as describes by King Solomon in;
"I rejoiced in them all, because Wisdom is their leader,
though I had not known that she is their mother."(Wisdom7:12)
In closing, Catholic Marian faithful knows the mystery of Christ life especially the hidden ones like your question by seeking the Wisdom of the Mother of Christ. We contemplate the Face of Christ thru the eyes of a Mother as Pope St.John Paul II The Great had teaches every catholic faithful must follow to gain knowledge and understanding.
Jesus is the First Advocate, and have to leave the Apostles within 40 days and said to them "Do not let your hearts be troubled" because Jesus First Mediation Act with the Abba Father is the sending of the Holy Spirit that will look upon or search who is worthy to become the "another Advocate" among those people present in the Upper Room.
The biggest mystery is who will the Holy Spirit choose to become the "another Advocate", as She will need a body like Jesus to manifest Her being as the Third Person of the Most Holy Trinity.
The answer was given by St.Alphonsus Liguori a Doctor of the Church.
"In His eagerness to show you,mercy, God has given His Son as your Advocate. And then to make your confidence even stronger, He has given you "another Advocate', who obtains through her prayers whatever she asks.Go to Mary, and you will see salvation. -St.Alphonsus Ligouri