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.