Is it permissible for the husband to take back his Italian Christian wife after divorcing her three times, knowing that he had taken her back after the first divorce, and problems subsequently arose that led to him divorcing her a second and third time?

Your wife has become unlawful to you and has been irrevocably divorced (Bainunah Kubra). She is not permissible for you unless she marries a valid marriage and her husband consummates the marriage with her, and then divorces her. This marriage must be a marriage of desire, not one for the purpose of making her lawful (tahlil). The utterance of divorce in a non-Arabic language is explicit according to the well-known madhhab (definition). It is advisable to encourage the woman towards Islam and introduce her to Islamic centers and seek assistance from righteous women, for guiding one man is better than red camels.