A sinner in hell does not have zōḗ aiṓnios, only an endless bíos. This distinction is forgotten by the JWs when they argue from the biblical statement that "eternal life," or zōḗ aiṓnios, is the privilege of the saved, then how "the wicked" can exist forever. However, this contrived opposition lacks the requirement of scholarly exegesis and is obviously an eisegesis born out of a compulsion to conform to the annihilationism adopted from Adventists.
The opposite of "eternal life," zōḗ aiṓnios, is not "eternal non-existence" in the sense of annihilation, but "eternal death," where "death" does not mean annihilation but separation from God. Thus, damnation is eternal 'bíos', mere existence without true "life" (zōḗ), i.e., without a relationship with God.
Like a small child that has abused its mother who loves it the most, we have all gone astray and haven't regarded the enormity of God and his creation as something and someone to be cherished and something to be grateful for.
Since our sin is against the eternal goodness of God, our punishment is eternal. Every day for eternity the lost or perished soul will experience existence without any trace of the goodness of God.
This is what Jesus warned people about over and over.
how can ye escape the damnation of hell? - Jesus
It is better for you to enter into life lame or maimed, rather than having two hands or two feet, to be cast into the everlasting fire. - Jesus