If the man was saved before the acts of adultery, yes, he is still saved after. But he's now a terrible witness for Christ.
Is that truly fair? We do have a witness to uphold but not a facade. There is a fine line between upholding our witness and hypocrisy. If anything, if this man repents, makes amends, and his wife through the love of God instilled in her, receives him back, what testimony does that give to the world? How could she forgive him? As God forgave her.
His witness isn't tarnished necessarily, but his character. That must be developed, as the Lord sanctifies him. His witness can be that of redemption through the forbearance of God, depending upon his wife albeit in the right to forsake him, deciding to stay with him. She can be an example of God's light in the darkness, and he in gratitude for being forgiven much will love much. A strengthening of their bond, though through unfortunate means.
Certain relationships have specific obstacles but through differences are they strengthened. They experience much together, and see what they have traversed. A tale not of woe, but woo. Cultivating a bond that isn't easily broken.
How can a sinner be a terrible witness for Christ, when it is they He has come for? The world may rejoice at a righteous man falling only being convicted of their own wrongdoing because what he professed he did not do but they knowing it is right do not try. If he is one of the righteous, of the light, then he will rise by the grace of God (maybe here, and definitely in the after).
Certainly the man is in the wrong. If he dares he ought to make it right. This only works if the wife is also too willing, not having him grovel and feel less, with something always over his shoulder but having forgiven him and seeking to restore or improve, what they once shared. If she can't forgive him, always uses his wrong as a weapon, there can't be reconciliation. He broke the bond, and she severs it (within her rights).