Herein lies a serious disagreement among sincere Catholics. A previous Catholic poster answered in the affirmative that there is time in Purgatory and Panevino also has affirmed the concept of time. However, you believe that Purgatory is timeless - without beginning and without end.
If that is the case, then anyone who is in an eternal state such as this will be there forever because there is no beginning nor end to it.
I'll comment. The problem with Gehenna is that God really didn't reveal a whole bunch about it beyond its name, its heat, and its unpleasantness. In that sense, it is much like the Trinity, which is not revealed by name. One can consult Scripture and find only the foundations for Trinity or Purgatory or Original Sin.
After that, there have been scholarly and religious efforts to flesh out the doctrines, but these are not as widely disseminated as, say, the Bible is, and they are not universally accepted, believed, or even thought about.
So, what you will discover on this topic and virtually every other one is that if you drill down, among Catholics there is only consistency of belief on the very broad overlays of the religion. Down in the details the Church does not insist on much, and Catholics are largely free to think about these things as their reason tells them.
Catholics agree on the creed, and they agree on a few other things, and after that the religion is quite individualistic.
One can contrast this with Protestantism, which has many branches, with each branch having a remarkable consistency of belief among its members - indeed, that is why they are members.
"Membership" means something different in Protestant Churches also.
Catholicism comes out of Judaism and shares many of its traits. In truth, Catholicism is the Judaism of the Temple, that existed at the time of Christ but ceased to exist in that generation - it is priestly, with sacrifice and sacrament. Protestantism came out of, and developed in reaction to, Catholicism, a millennium and a half later, and it was a product of the printing press.
The a priori of the religions are different, and it is more difficult for Catholics and Protestants to understand each other than it is for Catholics and Jews to understand each other. The religion IS the culture for Jewish and Catholic (Italian/Spanish, etc.) society, and culture comes from folk practice and tradition, not law, logic and books. Tradition is loose and broad and ingrained by habit and practice. It isn't all intellectually thought out - intellect merely serves to backfill and try to explain. Everything in Protestantism is thought out legalistically - including the decision to reject legalism, which is itself done legalistically.
Because of the very long history of bloodshed and hatred between Jews and Christians, with the Jews at the losing end of it after the 4th Century, there is always a great deal of friction and difficulty speaking across the Jewish/Christian lines. It's not impossible, but it's hard.
Because of the much greater violence, in modern times, in the Catholic/Protestant divide, there is less patience with each other, and far less desire to understand. There remains the desire to ACCUSE, to SCORN, to BELITTLE. And that quickly rears its head when Catholics and Protestants try to talk to each other about something like Purgatory.
I myself have found that when I try to discuss my religion the way I myself see it and live it, that there is very little common ground with Protestants, and that having the discussion is hard and quite unrewarding.