If a person's spouse continues in adultery then there is an obligation to divorce or separate, but I would recommend they remain single so restoration is possible. During that time they would be Eunuchs for the kingdom's sake. Likewise I think a believer should divorce or separate from their spouse only to not condone their unrepentant adultery, with the hope that they will repent and return.
Some people claim that once adultery occurs that the marriage can never be completely restored.
I don't agree. Hosea took back Gomer, God took back Israel, and according to Deut. 24 and Jer. 3 the divorced woman could return to her former husband unless she remarried. Even if she played the harlot she could still be taken back upon repentance if her husband wanted her.