Typically it is said the punishment in hell is eternal because offence is measured by the dignity of the one offended. Since God has infinite dignity then you sin is an infinite offence, and subsequently the punishment must be infinite. since man cannot feel infinite pain he instead is punished with infinite duration.
This logic has a problem. If a man bites a dog he commits a greater fault than if a dog bites a man, even though the man has greater dignity than the dog. (See second image, citation by William A Jurgens)
Pope Gregory the Great offers a stronger logic to why punishment in hell is eternal. The wicked if given eternal life would never cease to sin, they seek more to sin than to live. It is just that for those who willed never to be without sin must be punished without end, as he did not want any end to his crime.

