Im going to try to explain why hell is eternal from the Bible if i didn’t make things clear let me know.
1. Hell is eternal because God says it is.
Matthew 25:46 "And these shall go away into everlasting punishment: but the righteous into life eternal."
2. Hell is eternal because every action of ours has eternal ramifications.
Revelation 21:8 "But the fearful, and unbelieving, and the abominable, and murderers, and whoremongers, and sorcerers, and idolaters, and all liars, shall have their part in the lake which burneth with fire and brimstone: which is the second death."
3.Hell is eternal because the justice of God demands that the aggravation of sin be counterbalanced with a payment proportionable to the vidigation of Gods glory.
Romans 3:23 "For all have sinned, and come short of the glory of God;"
4. Hell is eternal because man was created in God's image and if man ever cease to exist God would be attacking his own image so when a person dies in their sin because they can never pay for their sin and God's image can never be destroyed hell must go on forever.
Genesis 2:7 "And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul."
5. Hell is forever because God would not be just if he did not give to sin what the demerit of sin calls for and if the demerit of sin call for Everlasting burnings the justice of God must give to sin what the demerit of sin calls for.
Deuteronomy 7:10 "And repayeth them that hate him to their face, to destroy them: he will not be slack to him that hateth him, he will repay him to his face."
I hope this answers the question. I suppose i could go into greater details if i need to.