Certainly, the Bible is clear that the fire and judgment of the wicked are eternal. Those who try to say otherwise deny the authenticity of God's word. But how could a merciful God burn people forever? The answer to this common question can only come through a proper understanding of the afore-mentioned texts, since the question stems from a misunderstanding of them and of the nature of God.
This misunderstanding results in an obvious scriptural dilemma regarding the nature of man versus eternal hell. If sinners burn forever, why are not all humans immortal? To state this another way, why are the righteous given "eternal life?" Going one step further, if sinners burn forever, and the righteous live forever, then are the sinners righteous? If both will live forever, then both have been given eternal life, or immortality, right?
In Deuteronomy 4:24 we find a big clue that can help us unlock the mystery. It says, "For the LORD thy God is a consuming fire, even a jealous God." What? God is a fire? So that explains why Moses saw a burning bush! And that explains the pillar of fire by night for the children of Israel in the wilderness! In fact, many others experienced the fire of God's presence throughout the Bible: the fire on the mountain for Elijah, the burning coal which touched Isaiah's lips, the tongues of fire above the apostles' heads. We might also remember the great fire of Nebuchadnezzar which failed to consume the three Hebrews whilst they walked in its flames with God.
God's promises also come with additional meaning when we understand this. The gold tried in the fire spoken of in Revelation may represent the characters of those who have cleansed themselves of sin through the indwelling presence of God. God's presence consumes sin like the dross. If only pure gold remains, it can stand in His presence. Now the promise of Isaiah that we will walk in the fire and not be burned holds richer meaning (Isaiah 43:2).
So, the righteous, like Daniel's three friends, will walk in the fire and not be burned. God is a consuming fire. His presence destroys sin. For those who have chosen to remain in sin, God's glory will consume them. Only the righteous will stand. However, since God is eternal, since God does not change (Malachi 3:6), and since He is a consuming fire, the fire will endure forever. Notice here that it is the fire which endures, not sin nor sinners. Sinners will never be granted immortality. They will receive the wages promised to them in Romans 6:23. In fact, sinners who were made to be immortal would likely punish themselves far more than God in His mercy will bring upon them in the lake of fire. The death which God's glory will bring to sin and to sinners will be a welcome relief to sinners and saints alike.