There is general agreement among Fathers, Doctors, and recent theologians that those punished in hell are incorrigible. In cases where some allowed or allow the possibility of a certain soul's or person's conversion (whether that conversion occur through the first time meeting with Christ in the case of pagans who did not know Christ on earth, through a medicinal, purifying penalty, or in some other way), they do not consider such a person doomed to everlasting punishment in hell.
However, there is less agreement on why those in hell are incorrigible. The common patristic account, when an account is given by those fathers who uphold everlasting punishment in hell, is that God has established this lifetime for grace and repentance, withholds his grace after death from those who died without charity, and therefore no conversion to God is then possible. Thus a person need not have fundamentally perverted their natural desire for good, need not be thoroughly bad, in order to punished in hell forever; it is enough to be overall more bad than good; one grave sin is enough.
The departed have not in the grave confession and restoration; for God has confined life and action to this world, and to the future the scrutiny of what has been done.
8. What shall we do in the day of visitation… when He will reason with us, and oppose us, and set before us those bitter accusers, our sins, comparing our wrongdoings with our benefits, and striking thought with thought, and scrutinizing action with action, and calling us to account for the image which has been blurred and spoilt by wickedness, till at last He leads us away self-convicted and self-condemned, no longer able to say that we are being unjustly treated — a thought which is able even here sometimes to console in their condemnation those who are suffering….
9. … [His right judgment] places in the balance for us all, our entire life, action, word, and thought, and weighs against the evil that which is better, until that which preponderates wins the day, and the decision is given in favor of the main tendency; after which there is no appeal, no higher court, no defense on the ground of subsequent conduct, no oil obtained from the wise virgins, or from them that sell, for the lamps going out, no repentance of the rich man wasting away in the flame, and begging for repentance for his friends (St. Gregory Nazianzen, Oration 16).
Recent theologians (possibly including Joseph Ratzinger), reluctant to affirm that the incorrigibility of those in hell is due to God's hardening their hearts in sin through a withdrawal of their grace, commonly hold that only those are in hell who have so distorted and perverted their will through deliberate sin, that it is impossible for them to convert, or impossible without a strict miracle. Thus only persons who became thoroughly bad in this life are in hell.
A middle position might be that in the moment of death God's love is so encountered that persons, depending on their life up till then and their state at that moment, necessarily either accept God's love, or so forcefully reject it that they thereby become thoroughly bad, even if previously they were not so, but had just failed to subordinate some true good to God.
It seems necessary to take one of these positions. Man's first, original will has to be good, since it is a natural will, from God, the creator of nature. And all man's particular choices and voluntary acts derive from this first original will for goodness, which must, just considered in itself, remain, as long as man's nature remains. Hence, man must remain capable of conversion to the true good, if guided through the right influences. Thus incorrigibility must be due either to God's taking away the possibility of those influences (a hardening of man's heart), or man's being in himself so set in evil that he is utterly closed to those influences that could otherwise draw him to good through his first and natural desire for goodness.
I don't know if moderns including Popes have too much weight in this area. Both John Paul II and Benedict expressed the thought that we could not be certain that Judas is in hell (Augustine and Chrysostom were certain Judas was in hell presumably based on Christ's words about Judas being inappropriate words if said about anyone bound for glory even through a lengthy purgation). Karl Rahner and perhaps Balthasar also implied the same about Judas in their hopes for an empty hell based on God's antecedent will that all men be saved. Aquinas however stated: " The antecedent will of God does not always take place"…but His will simply…always takes place.
Both John Paul II and Benedict also in line with that Judas position, punished almost no one in respect to the sex abuse period. They're not alone. The U.S. punished
almost no one in regard to the financial CDO's that almost destroyed the US economy
and did so for the 9% unemployed to this day. In these CDO's, top quality mortgages were bundled with low quality mortgages and top ratings agencies labeled them AAA….and neither the bundlers nor the ratings agency people were arrested.
Then there's the death penalty U turn of the last two papacies based on the novel idea that secure life sentences are brand new. Ahem….Rome had the damnatio
ad metallum….damned to the mine from which lifers could not make phone calls to have witnesses murdered out on the street. The Avignon papacy had a fortress with walls 17 feet thick. I suspect their prisons were similar.
In short modern man….both papal and non papal in the West seems squeamish about final punishment….whether execution or hell. (Japan has the death penalty and was listed recently as the third safest country in the world vis a vis murder….though that has also to do with ethnic homogeneity and island isolation and lack of a deprived class.)
That some Bible verses are pivotal…here a person switches fundamental options….Ezekiel 18:24:
"But if the upright abandons uprightness and does wrong by copying all the loathsome practices of the wicked, is he to live? All his upright actions will be forgotten from then on; for the infidelity of which he is guilty and the sin which he has committed, he will most certainly die."
and the opposite switch:
27 "Similarly, when the wicked abandons wickedness to become law-abiding and upright, he saves his own life."
We must remember that purgatory is not a default setting but is a reward for at least being in sanctifying grace. In light of that, excepting hidden insanity, it is hard to see how millions of criminals e.g. throughout history who died in the act of crime or during apprehension as they tried to kill law enforcement personnel…..all end up in Heaven ala those modern theologians who dare hope for an empty hell.
ps
In answer to your title, Aquinas in one place in the ST suggested that hell is eternal because the mortal sinner turns away from the One who is eternal. He noted that there are two turnings in mortal sin: turning toward a mutable good…and…turning away from God. The degree of hell's punishment derives from the former and the eternity of hell's punishment derives from the latter.
"Recent theologians (possibly including Joseph Ratzinger), reluctant to affirm that the incorrigibility of those in hell is due to God's hardening their hearts in sin through a withdrawal of their grace, commonly hold that only those are in hell who have so distorted and perverted their will through deliberate sin, that it is impossible for them to convert, or impossible without a strict miracle. Thus only persons who became thoroughly bad in this life are in hell."
This definitely fills me with hope. In a way, it's comforting for me to know that even if I sin once in awhile God will not damn me as long as I don't become thoroughly corrupt like, say, Hilter or Stalin.