Objection 1. It would seem that the husband is bound by precept to put away his wife who is guilty of fornication. For since the husband is the head of his wife, he is bound to correct his wife. Now separation from bed is prescribed as a correction of the wife who is guilty of fornication. Therefore he is bound to separate from her.
Objection 2. Further, he who consents with one who sins mortally, is also guilty of mortal sin. Now the husband who retains a wife guilty of fornication would seem to consent with her, as stated in the text (Sent. iv, D, 35). Therefore he sins unless he puts her away.
Objection 3. Further, it is written (1 Corinthians 6:16): "He who is joined to a harlot is made one body." Now a man cannot at once be a member of a harlot and a member of Christ (1 Corinthians 6:15). Therefore the husband who is joined to a wife guilty of fornication ceases to be a member of Christ, and therefore sins mortally.
Objection 4. Further, just as relationship voids the marriage tie, so does fornication dissolve the marriage-bed. Now after the husband becomes cognizant of his consanguinity with his wife, he sins mortally if he has carnal intercourse with her. Therefore he also sins mortally if he does so after knowing her to be guilty of fornication.
Objection 5.On the contrary, A gloss on 1 Corinthians 7:11, "Let not the husband put away his wife" says that "Our Lord permitted a wife to be put away on account of fornication." Therefore it is not a matter of precept.
Objection 6. Further, one can always pardon the sin that another has committed against oneself. Now the wife, by committing fornication, sinned against her husband. Therefore the husband may spare her by not putting her away.
I answer that, The putting away of a wife guilty of fornication was prescribed in order that the wife might be corrected by means of that punishment. Now a corrective punishment is not required when amendment has already taken place. Wherefore, if the wife repent of her sin, her husband is not bound to put her away: whereas if she repent not, he is bound to do so, lest he seem to consent to her sin, by not having recourse to her due correction.
Reply to Objection 1. The wife can be corrected for her sin of fornication not only by this punishment but also by words and blows; wherefore if she be ready to be corrected otherwise, her husband is not bound to have recourse to the aforesaid punishment in order to correct her.
Reply to Objection 2. The husband seems to consent with her when he retains her, notwithstanding that she persists in her past sin: if, however, she has mended her ways, he does not consent with her.
Reply to Objection 3. She can no longer be called a harlot since she has repented of her sin. Wherefore her husband, by being joined to her, does not become a member of a harlot. We might also reply that he is joined to her not as a harlot but as his wife.
Reply to Objection 4. There is no parallel, because the effect of consanguinity is that there is no marriage tie between them, so that carnal intercourse between them becomes unlawful. Whereas fornication does not remove the said tie, so that the act remains, in itself, lawful, unless it become accidentally unlawful, in so far as the husband seems to consent to his wife's lewdness.
Reply to Objection 5. This permission is to be understood as an absence of prohibition: and thus it is not in contradistinction with a precept, for that which is a matter of precept is also not forbidden.
Reply to Objection 6. The wife sins not only against her husband, but also against herself and against God, wherefore her husband cannot entirely remit the punishment, unless amendment has followed.
Source: Summa Theologica (New Advent)