I recall that when I was in college a theology professor addressed this problem. He said the reason that finite sin brings about infinite punishment is because it is committed against an infinite God. It is not so much what you did but Whom you did it against. Your sin can be quantified but God cannot. I think I speak for many when I say that this solution is not intuitively satisfying.
Later a seminary professor made an intriguing suggestion. He said that, though he could not prove it conclusively from Scripture, he suspected that hell is full of people who keep on sinning. They refuse to learn, they do not repent, they choose to continue to rebel against God rather than submit to his will. So their ongoing sin is met with ongoing punishment.
He may have a point. Revelation 16:9-10 speaks of people who, though they suffer apocalyptic judgment, curse God and do not cry out to him for mercy or change their ways. They prefer opposition and its pains to submission and its joys. Maybe hell is like that.
I have another idea though that I would like to throw at the problem. It has to do with time and how we experience it. Perhaps it might prove helpful to put the question of hell's duration (or heaven's, for that matter) in the context of how we understand time.
I told my brother about a thought that popped into my head a month or so after our father passed away suddenly from a heart attack. I was a junior in high school. Our mother grieved with a sorrow inconsolable. Mom and Dad were best friends, and never in my life have I known a marriage better than theirs. So she struggled when he was taken away suddenly. She said to me through tears, "I know that this is wrong and selfish of me, but I think, 'How can he enjoy heaven now if I'm not there with him? How could that be heaven for him?'" An answer came to me in a flash. I said, "Maybe when Dad got to heaven he saw you there." I explained as best I could that, maybe, when we die, we get off the timeline of earthly history and are carried above it into an eternal state. If that is the case, then heaven is not to be understood as a place where people are arriving little by little over the course of thousands of years. Maybe the redeemed are all there at once.
She liked that answer, and I am glad that it comforted her. Is it true? I don't know. We'll find out some day. I would be the first to admit that it cannot be reconciled with literal interpretations of the rich man and Lazarus in Luke 16:19-31 or the martyred souls under the altar in Revelation 6:9-11. But there are several orthodox doctrines that cannot be reconciled with literal readings of those texts. Everyone acknowledges they are symbolic to some degree. (For example, how can souls, which are immaterial, be "under" an altar?) The question is, "How symbolic are they, and to what extent and in which directions?" and that probably is not easy to determine. The realities of heaven and hell can only be communicated to us in terms of our earthly experience. Everything that is true about them must be transposed down to our limited categories, like a Mozart symphony played on a kazoo.
Maybe one of our limited categories is time. We experience personal reality as a succession of moments which we call time, and have difficulty even imagining any other kind of existence. But I'm pretty sure that God exists outside time. I'm pretty sure that time, like the universe itself, is something that he created and is not bound by. If the timeline of history can be imagined as the pages of a book, then we live our lives on (let's say) page 172. The previous 171 pages are history as we know it, and the following pages are, to us, future and unknown. But God holds the whole book in his hands. He can open it to any page. He can even write himself into the book as a character, as he did in the incarnation of Jesus Christ.
I wonder if, when we die, we get off the pages of that book and are joined to God's eternal state. If that is true, then the reality of the afterlife is not quite like an endless series of pages in a book that is already very long. It is not like living a billion quadrillion pages followed by a billion quadrillion more. Maybe it is more like seeing that book of time, and a good many other things besides, from the perspective of a good and loving God.
Somewhere I think C. S. Lewis speaks of our experience of reality as something like traveling on a train. Suppose you get on a train and travel from Chicago to Glacier National Park, as my wife and I did a couple years ago. The scenery zips by you, and you enjoy to some extent the sights from the window as the train moves on. But that's the problem: the train always moves on. You long for it to stop, to reach its destination so you can get off and explore delights on either side of the uni-dimensional track. If heaven were as time-constrained as earth, then its endless succession of days might be compared to a train that never stops, a journey that never ends. It lasts a long time, and you never get off the track. But what if heaven were more like a destination than a journey? In this life, we can never fully explore a good moment, no matter how ecstatic it is. Every moment flits through our fingers and is converted into a memory. You can never hold on to it. Poets talk about trying to possess those moments and re-create them for the sake of ongoing joy. ("If I could save time in a bottle"; "Some day...I will feel a glow just thinking of you, and the way you look tonight"). What if, in heaven, we don't have to take a quick snapshot of the scene outside our window and cling to the memory of it by means of a photograph because now, at last, the train has stopped and we can actually go there?
I suspect, though I cannot prove, that the afterlife is not so much a matter of endlessly succeeding days as it is a destination that is either granted by grace or deserved by sin. Its eternality, when transposed into the language of time-bound persons, becomes "lots and lots of years" because the only alternative (again, for time-bound people) is "death" or "non-existence", and it certainly isn't that.
The other day I received a jolt of joy as I listened to physicist Brian Greene explain the extraordinary implications of the nature of time as Einstein helped us to understand it. If you have ever listened to that stuff about relativity, you will know that it is practically impossible to wrap your mind around the paradoxes and anti common-sense notions that physicists now know to be true. At one point, Greene defined time as "that which allows us to see that something has changed." I saw that as a beautiful definition with theological implications that Christians can receive gladly. God does not change. James 1:17 says, "Every good and perfect gift is from above, coming down from the Father of the heavenly lights, who does not change like shifting shadows." Hebrews 13:8 says, "Jesus Christ is the same yesterday and today and forever." Our eternal God is not governed by time which, by its very nature, requires change in order to be perceived, or even to exist. Perhaps, when we die, we will not be governed by time either. Perhaps instead we will arrive at the destination that our will or his grace has chosen: wretched alienation from him, or blessed union with him.