One of the nicest heresies in the world today is the belief that, rather than lasting forever, Hell actually has an expiration date. Those who are condemned will eventually be completely consumed by the fire and die, ceasing to exist.
Unfortunately, the Bible blocks this interpretation in a number of ways. When Jesus preached about Hell, He never mentioned an end to the torment. Quite the opposite, He compared it to the eternal life received by the righteous. Just as we, as believers, receive eternal life, the impenitent suffer eternal punishment. This features things that are not possible if consciousness is lost. The wicked cannot weep, or gnash their teeth (e.g. Matthew 25:30) if they are unconscious. Nor can they be tormented without rest day and night forever and ever (Revelation 20:10-15).
Annihilationism, a.k.a. Conditional Immortality, argues that this cannot be the case, because the wicked are said to face death. Jesus even tells us that those who do not believe in Him "will not see life" (John 3:36). Now, already we hit a problem: The wicked will see the resurrection (e.g. Daniel 12:2). Thus, we see that the Annihilationist interpretation depends on a faulty understanding of what exactly death is.
The meaning of "death" varies from culture to culture. Here in the West, we have been heavily influenced by secular culture. In atheism, death really is the cessation of consciousness. However, only certain sects of Judaism agree. In Jesus' day, that sect was the Sadducees, (Matthew 22:23). Yet, to these people, Jesus had the following message: "You are in error because you do not know the Scriptures or the power of God. (...) have you not read what God said to you, ‘I am the God of Abraham, the God of Isaac, and the God of Jacob’? He is not the God of the dead but of the living.”" (See Matthew 22:23-33).
The Sadducees believed, as do modern atheists, that death is the final end. The living die, after which their consciousness ceases forever, and they are never to be raised. Jesus says that actually, God, who is currently the God of Abraham, Isaac, and Jacob (who are dead) is not the God of the dead, but the living. Therefore, though Abraham, Isaac and Jacob are dead in this life, they are alive in some other sense. That is, spiritually.
We actually see several indications of this in Scripture. Paul, for example, says that to be absent from the body is to be present with Christ (2 Corinthians 5:8). He even believed this to the point where he desired to do so (Philippians 1:23), only remaining here because he believed the Church on earth had a greater need of him. Paul clearly did not believe that to kill a Christian is to end his consciousness. Furthermore, there are several examples that prove this to be the case. When the witch raised Samuel, did she bring up his physical body? No, she brought up his spirit (1 Samuel 28:13). Moses died in Moab (Deuteronomy 34:5), yet he was present at the Transfiguration. Jesus told the penitent thief "I tell you the truth, today you will be with me in Paradise" (Luke 23:43), and yet he died on the cross next to Jesus.
Furthermore, in Luke 16, we read a story of a rich man and a beggar named Lazarus. In this story, both men die. The beggar is taken to Abraham's side, whereas the rich man is trapped in Hades. All three, though dead on the earth, are conscious in this realm of the dead. Now, we could spend hours debating whether or not this is a true story, or just one more parable. I personally am leaning towards it being a real event, but it could just as easily be a parable. The fact is, it describes a Jewish understanding of what happens after death: The spirits of the dead are divided by a great chasm into two regions of Sheol. On one side of the chasm, Paradise, where the righteous receive their reward. On the other side, Hades, where the wicked are tormented in fire, longing for just a drop of water to cool their tongue.
So, clearly, life and death are not directly linked to consciousness. There are certain verses that can be made to suggest otherwise (most of which are in Ecclesiastes), but without wanting to get into too much depth on those in this article, suffice to say the Bible does not define life as consciousness, nor death as the end of consciousness. Rather, you can be alive and unconscious, and you can be dead and conscious. So, what is death if not the cessation of consciousness?
The Bible actually presents death as a separation. Physical death is the separation of the spirit from the body (James 2:26). Spiritual death is the separation of man from God's favor due to sin, be that on the earth (Ephesians 2:1) or in Hell (Revelation 20:14). As Christians, we are actually called to be "dead to sin" (Romans 6:11). What about life? Simply reverse that. If death is a separation from the body, or from God's favor, then life is the union of the spirit and the body, or the reception of God's favor. Heaven is considered eternal life because nothing that should remain united will ever be separate again. The spirit of a heavenly being cannot be separated from the body, neither will sin ever separate a man from God again. By contrast, those in Hell will always be separated from God and His blessings, never having the chance at redemption. Thus, while conscious, they are dead.
Ultimately, while Annihilationism is a nice doctrine, it cannot be considered true, because it requires the unorthodox reinterpretation of a number of Biblical statements. Sadly, there will be many people who will be tormented day and night forever and ever in the lake of fire. Rather than cause us to reject God's Holy word, this should motivate us to ensure as few people as possible suffer this fate.