If God's power isn't keeping them alive, then what is? Are there eternal things beyond God? outside of God?
If God's power is keeping them alive, then what purpose could it possibly serve, since they can't do anything except to feel pain?
The idea that those "in hell" experience a kind of active external torment is, broadly, a fairly Western conception. In the Christian East the views of hell have been different.
When the Eastern Orthodox talk about hell, they aren't talking about a separate "place" from heaven, but rather conceive of both "heaven" and "hell" as being the same "place". It's not about "place" at all really, but rather how a person experiences God's presence. And so what makes heaven heaven is the same thing that makes hell hell: God's love.
Essentially, it is the person's own disposition toward God that makes heaven heaven or hell hell. The 7th century Christian bishop of Nineveh, St. Isaac the Syrian, described the anguish of hell as an anguish of bitter regret, comparing it to our own experience here on earth when we have betrayed and hurt a dear friend--that remorse, that regret, that internal torment we experience knowing what we have done--that is the torment or anguish of hell. So that when God loves, it is a bitter pain.
A rather consistent stream of thought, both East and West, about hell throughout history is that hell is a choice. That often sounds bizarre--after all, who in their right mind would choose hell? But it shouldn't be that far fetched of an idea, after all, we consistently and frequently make choices in this life which are hurtful, harmful, and even destructive toward ourselves. We hold grudges, sometimes for years or even decades, we don't let go of anger and resentment; we hold onto destructive feelings all the time and often resist the things that will help us heal, like therapy. Sure, nobody says, "I think I want to be tortured forever", but how many choose to be angry and miserable day after day? That's hell. It's not God throwing people into a dark pit and then letting devils with pitchforks poke and prod them forever, it's the clinging onto of misery, anger, resentment.
As C.S. Lewis would phrase it, the gates of hell are locked from the inside. It is those "in hell" who shut themselves up, there is no warden keeping them imprisoned.
What has been an open question throughout the history of Christianity is if redemption remains available for those "in hell". There's no real answer to that question, though many different Christians have given diverse opinions over the centuries. Some argue that it is impossible for those in hell to eventually be reconciled to God; and some have gone so far as to argue that it is possible that ultimately all will be reconciled to God. But it's a question that has no dogmatic answer within Christianity (broadly speaking).
-CryptoLutheran