Is the wife considered irrevocably divorced (three pronouncements of divorce) and thus unlawful to her husband, after he uttered a conditional oath of divorce to her (which he counted as one pronouncement and took her back), then divorced her a second time and took her back, then divorced her a third time while she was menstruating, having forgotten about that?

A conditional divorce has two scenarios: Either the intention is divorce, in which case it takes effect immediately upon the occurrence of the condition, or the intention is merely a threat. This [latter case] is considered a divorce by the majority of scholars, while some hold that it does not constitute a divorce and requires an expiation for a broken oath (kaffarat yameen).

The husband's uncertainty about his intention (threat or divorce) does not change anything according to the majority of scholars. However, for those who do not consider a threatened divorce to take effect, doubt does not cause the divorce to occur.

Divorce pronounced during menstruation is considered valid by the majority of scholars. Accordingly, the wife has become irrevocably divorced (bainunah kubra), and she is not permissible for her husband [to remarry] until after another marriage [to a different man].