Conditional immortality (or annihilationism) is a heterodox belief which states that obtaining immortality is based upon a condition, namely believing the gospel. Therefore, unbelievers don’t suffer eternally in hell for their sin but rather (after a time of punishment) cease to exist. Atheists generally believe that at death consciousness dissolves and individual persons cease to exist as well. Conditional immortality basically affirms this atheistic belief.
I’m not going to make an extended argument here for what has been called the traditional view of hell. My only purpose is to state that before I believed the gospel, I was told by someone that if I didn’t believe it I would die and be eternally extinguished. My very first thought was, “Who cares? I won’t exist. I can have my sin and (someday in the future) die and go to sleep forever.”
In other words, the doctrine of conditional immortality doesn’t properly take into account man’s total depravity. Fear of death is a weak motivation for repentance. Fear of hell, that’s quite another motivation.