Neither does the wrath of God. Scripture doesn't say that the have no rest day or night forever.
Rev 14:11 And the smoke of their torment ascends forever and ever; and they have no rest day or night, who worship the beast and his image, and whoever receives the mark of his name.
It says the smoke ascends forever and ever. It doesn't say they have no rest forever and ever. You're reading that into the second part.
Rely on you insertion of punctuation if you want but the Greek doesn't have any. I'll go with the Greek as well as other passages which I notice you conveniently ignore.
Matthew 25:46 And these shall go away into everlasting punishment: but the righteous into life eternal.
2 Thessalonians 1:9 Who shall be punished with everlasting destruction (olethros) from the presence of the Lord, and from the glory of his power;
olethros - 3639 /ólethros ("ruination") however does not imply "extinction" (annihilation). Rather it emphasizes the consequent loss that goes with the complete "undoing." [http://biblehub.com/greek/3639.htm]