As is commonly known, the Jehovah's Witnesses and Seventh-Day Adventists both deny the doctrine of a conscious, eternal punishment in Hell. Rather, they advocate a doctrine commonly known as "annihilationism," the belief that the wicked will be destroyed at the judgment. Thus, the punishment would be instantaneous, rather than eternal. There are other groups that also teach this doctrine, but the Witnesses and the Adventists are the best known.
The proper question is, Is their claim biblical? They would agree with me that this is the proper issue. They would say "yes," but I would definitely say "no." Why do I hold my opinion? One reason is Isaiah 48:22: "'There is no peace,' says the Lord, 'for the wicked.'" This isn't my only reason; for more, use the "annihilationism" tag at the bottom of the this article.
"There is no peace," say the prophet. They will have no respite from their judgment. And this isn't what some people claim, an eternal punishment for a limited time of sin. I agree, that would be unjust. Rather, those in Hell have all their restraints of culture and upbringing removed, and give free vent to their hatred of God. Just as they continue to curse Him for eternity, they continue to suffer the consequences for eternity. "There is no peace." Is that not the moral of the story of the Rich Man and Lazarus (Luke 16:19-31)? notice that the Rich Man never asks to be released from Hell. Rather, he asks for a modicum of relief, just a drop of cooling water (verse 24). And even that he doesn't want from Jesus - because he despises Him - but rather from Lazarus! Yet, he is denied even this minuscule respite, for "there is no peace for the wicked."
3GT Episode 73: When Two Kingdoms Become One
4 hours ago