For all except the sons of perdition this suffering is eternal only in the sense that it is God’s suffering and he is eternal (see D&C 19:4-12).
It will come to an end at the time of the second resurrection (at the end of the Millennium). The sons of perdition, those who have known the power and goodness of God and who then deny and defy that power, shall indeed suffer in outer darkness forever.
For those who reject the gospel and sneer at its saving power, it is as though there had been no redemption made, as though Christ had never come into the world, as though there had been a Fall but no hope for deliverance from it.