The Ante-Nicene Fathers provide a variety of viewpoints on this matter. As with so many other topics, there was lively disagreement among their ranks.
I'll loosely group ideas into 3 broad categories, and offer examples of each:
- Continuation of authority
- Reduction in authority
- Rampant apostasy
Continuation of authority
Irenaeus of Lyons (late 2nd century) is among the most commonly cited fathers for support for apostolic succession. 3 of his more emphatic statements are provided below.
In refutation of the teachings of those he considered heretical he appealed to the authority of Rome:
...tradition derived from the apostles, of the very great, the very
ancient, and universally known Church founded and organized at Rome by
the two most glorious apostles, Peter and Paul; as also the faith
preached to men, which comes down to our time by means of the
successions of the bishops. For it is a matter of necessity that every
Church should agree with this Church, on account of its preeminent
authority (Against Heresies 3.3.2).
He cites Clement of Rome as a successor to the apostles and the author of a letter teaching apostolic truth:
...in the third place from the apostles, Clement was allotted the
bishopric. This man, as he had seen the blessed apostles, and had been
conversant with them, might be said to have the preaching of the
apostles still echoing [in his ears], and their traditions before his
eyes. Nor was he alone [in this], for there were many still remaining
who had received instructions from the apostles. In the time of this
Clement, no small dissension having occurred among the brethren at
Corinth, the Church in Rome dispatched a most powerful letter to the
Corinthians, exhorting them to peace, renewing their faith, and
declaring the tradition which it had lately received from the apostles
(Against Heresies 3.3.3)
After relating the succession of Roman Bishops from the 1st century down to his own time, Irenaeus states:
In this order, and by this succession, the ecclesiastical tradition
from the apostles, and the preaching of the truth, have come down to
us. And this is most abundant proof that there is one and the same
vivifying faith, which has been preserved in the Church from the
apostles until now, and handed down in truth. (Against Heresies 3.3.3)
Though Irenaeus does not use some of the vocabulary of apostolic succession that would be developed in later years, it is not difficult to see how his statements can be interpreted in favor of apostolic authority being handed down through a succession of Bishops.
Tertullian of Carthage (late 2nd century)
As already noted by SupportiveDante, Tertullian emphasized that the church leaders of his day could trace their authority to the apostles:
Let them produce the original records of their churches; let them
unfold the roll of their bishops, running down in due succession from
the beginning in such a manner that [that first bishop of theirs ]
bishop shall be able to show for his ordainer and predecessor some one
of the apostles or of apostolic men...
For this is the manner in which the apostolic churches transmit their
registers: as the church of Smyrna, which records that Polycarp was
placed therein by John; as also the church of Rome, which makes
Clement to have been ordained in like manner by Peter. In exactly the
same way the other churches likewise exhibit (their several worthies),
whom, as having been appointed to their episcopal places by apostles,
they regard as transmitters of the apostolic seed. (Prescription
Against Heretics ch. 32)
Reduction in authority
Ignatius of Antioch (an Apostolic Father) had much to say about church structure and the importance of respecting church authorities. He was also very careful to acknowledge that he, as a Bishop, was not an apostle and did not have the authority to speak as they had.
Several excellent examples of his views are expressed in his letter to the Trallians:
without the bishop ye should do nothing, but should also be subject to the presbytery, as to the apostle of Jesus Christ (chapter 2)
reverence the deacons as an appointment of Jesus Christ, and the bishop as Jesus Christ, who is the Son of the Father, and the presbyters as the sanhedrin of God, and assembly of the apostles. Apart from these, there is no Church (chapter 3)
continue in intimate union with Jesus Christ our God, and the bishop, and the enactments of the apostles. He that is within the altar is pure, but he that is without is not pure; that is, he who does anything apart from the bishop, and presbytery, and deacons, such a man is not pure in his conscience. (chapter 7)
(note that writing circa AD 107 Ignatius strongly implies that there are no longer apostles in their midst, as it is bishops, presbyters, and deacons who must be consulted, and without whom there is no church. This statement could hardly be made if the church was still being led by apostles)
But shall I, when permitted to write on this point, reach such a height of self-esteem, that...I should issue commands to you as if I were an apostle? (chapter 3)
From his Epistle to the Romans:
I do not, as Peter and Paul, issue commandments unto you. They were apostles of Jesus Christ, but I am the very least (chapter 6)
Ignatius is clear that the officials of the church have authority and ought to be respected, but he repeatedly acknowledges that they are not apostles, cannot speak as apostles, and cannot replace that which was given by the apostles.
Finally, from his epistle to the Magnesians:
your bishop presides in the place of God, and your presbyters in the place of the assembly of the apostles (chapter 6)
The parallelism shows that as the bishop is clearly lower in authority than God, the presbyters are lower in authority than the apostles (see also his deference to higher, apostolic authority in Trallians ch. 10 & Ephesians ch. 11).
Clement of Rome (another Apostolic Father) also acknowledged the authority of the bishops & deacons came from the apostles, but does not treat these officials as replacements of the apostles--their position is lesser & distinct:
1 The Apostles received the Gospel for us from the Lord Jesus Christ;
Jesus Christ was sent forth from God.
2 So then Christ is from God, and the Apostles are from Christ. Both
therefore came of the will of God in the appointed order.
3 Having therefore received a charge, and having been fully assured
through the resurrection of our Lord Jesus Christ and confirmed in the
word of God with full assurance of the Holy Ghost, they went forth
with the glad tidings that the kingdom of God should come.
4 So preaching everywhere in country and town, they appointed their
firstfruits, when they had proved them by the Spirit, to be bishops
and deacons unto them that should believe. (1 Clement 42:1-4)
By Clement's time the apostles' appointees were bishops & deacons; not successor apostles.
Cyprian of Carthage (3rd century)
Each had been bent on improving his own patrimony, and had forgotten
what believers had done under the Apostles, and what they ought always
to do. They were brooding over the arts of amassing wealth; the
pastors and the deacons each forgot his duty; works of mercy were
neglected, and discipline was at the lowest ebb...fraud and deception
practiced among brethren....
Even many bishops, who ought to be guides and patterns to the rest,
neglected the peculiar duties of their stations, gave themselves up to
secular pursuits. They deserted their places of residence and their
flocks; they traveled through distant provinces in quest of pleasure
and gain; gave no assistance to their needy brethren, but were
insatiable in their thirst of money. They possessed estates by fraud
and multiplied usury.
What have we not deserved to suffer for such conduct? Even the divine
word hath foretold us what we might expect: “If his children forsake
my law and walk not in my judgments, I will visit their offenses with
the rod and their sins with scourges.” These things had been denounced
and foretold but in vain. Our sins had brought our affairs to that
pass, that because we had despised the Lord’s directions, we were
obliged to undergo a correction of our multiplied evils and a trial of
our faith by severe remedies. (as quoted in End of Religious
Controversy, Milner, Letter 26)
In rejecting the authority of any other bishop over himself he wrote:
I marvel that some, with daring temerity, have chosen to write to me
as if they wrote in the name of the Church (The Ante-Nicene Fathers
As summarized by Tad R. Callister:
On one occasion...Stephen [Bishop of Rome] attempted to asssert his
general command over the African Council of Bishops on the issue of
whether or not a heretic needed to be rebaptized. In AD 258, Cyprian
the bishop of Carthage, called a council of eighty-seven bishops to
discuss a response to what Cyprian called "the bitter obstinacy of our
brother Stephen." As part of their response, these bishops expounded
that there was no successor to Peter there was no pope, and there was
no supreme bishop. (The Inevitable Apostasy p. 61)
Eusebius of Caesarea (3rd-4th century) lamented:
the ambitious aspirings of many to office, and the injudicious and
unlawful ordinations, that took place, the divisions among the
confessors themselves, the great schisms and difficulties
industriously fomented by the factions (HE Martyrs of Palestine ch. 12)
Hippolytus of Rome (3rd century):
And he [Callistus, bishop of Rome] first invented the device of
conniving with men in regard of their indulgence in sensual pleasures,
saying that all had their sins forgiven by himself...should he commit
any transgression; the sin, they say, is not reckoned unto him,
provided only he hurries off and attaches himself to the school of
Callistus. And many persons were gratified with his regulation. (The
Ante-Nicene Fathers 5:131)
The very bishops of the church expressed tremendous distrust that the leaders of the church in their time were acting in accordance with God's will, doctrine, or authority.
My own interpretation of this evidence (aka HoldToTheRod's ravings):
- The earliest writers acknowledge the apostles had appointed stewards over various responsibilities in the church, but had not appointed successors with apostolic authority. Their focus is on following the teachings given and the officers appointed by the apostles.
- A generation later, Irenaeus sees schism and fracturing and heresy, and promotes a hierarchical structure to avoid fragmentation of Christianity
- By the third century, disarray and apostasy were abundantly evident
My own personal view, as one who believes in the doctrine of priesthood keys, is that the apostles did indeed appoint Bishops and others as stewards of various churches, but with the departure of the apostles, the keys to administer the church collectively, or to appoint successors for subsequent generations, were no longer on the earth.
It appears that Polycarp of Smyrna was the last known Bishop who was appointed by apostolic authority; he did not have apostolic authority to appoint his own successor. If John's departure (circa AD 100) marks the end of apostolic leadership of the general church, Polycarp's death (circa AD 155) can perhaps be considered the end of local church leadership under anyone authorized by the apostles.
God withdrew apostolic authority due to apostasy, necessitating a subsequent restoration.
Acknowledgement to Ante-Nicene Father quotations compiled by earlychristianwritings.com, newadvent.org, & The Inevitable Apostasy by Tad R. Callister