The Bible does and I can defend this doctrine because I already have.
Yes. The Bible is clear that they who are cast into the lake of fire will suffer day and night forever.
Revelation 19:20, "And the beast was taken, and with him the false prophet that wrought miracles before him, with which he deceived them that had received the mark of the beast, and them that worshipped his image. These both were cast alive into a lake of fire burning with brimstone."
Revelation 20:10, "And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever."
Matthew 25:41, "Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels:"
You could interpret it as meaning that the devil will be thrown into the pit to be tormented forever, and the flames that burn them are eternal. It never says sinners will be eternally punished, only that Hell will forever exist.
Why should God show favoritism towards men and annihilate them while punishing angels in hell eternally? Why should angels suffer and men not suffer? It could be argued that angels got men to do something wrong but why punish one group and not the other? Men sinned willingly and all sin is wilful. Men committed all the violence in this world and it can be argued that angels did not.
Romans 2:11 For God does not show favoritism.
Acts 10:34 ¶ Then Peter opened his mouth, and said, Of a truth I perceive that God is no respecter of persons:
Jude 1:13 Raging waves of the sea, foaming out their own shame; wandering stars, to whom is reserved the blackness of darkness for ever.
metaph. of ignorance respecting divine things and human duties, and the accompanying ungodliness and immorality, together with their consequent misery in hell
That word "ever" is also interesting. It means "forever".
Anyway, you can throw whatever arguments before me, CorvusRexus. Annihilationism is false doctrine and I already have it covered but I took time here to make a new argument because I'm not satisfied with doing enough.
Notes:
Blue Letter Bible - Lexicon
Jude 1 (Blue Letter Bible: KJV - King James Version)
Blue Letter Bible - Lexicon