Existentialism scars our thinking into believing death means annihilation. Death is simply a state of existence involving separation.
Too many people grieve themselves at the loss of a loved one, grieving for their separation from themselves, but then confusing their separation with annihilation.
And eternal punishment is not only separation from God, but from anything positive while realizing proactive punishment.
"And he cried and said, Father Abraham, have mercy on me, and send Lazarus, that he may dip the tip of his finger in water, and cool my tongue; for I am tormented in this flame. But Abraham said, Son, remember that thou in thy lifetime receivedst thy good things, and likewise Lazarus evil things: but now he is comforted, and thou art tormented." (Luke 16:24-25)