Is it permissible to reconcile with a wife who has been divorced three times after she refused to mend her ways and insisted on divorce?

It is not permissible for a man to take back his wife after divorcing her three times, because Allah Almighty says: "And if he has divorced her [for the third time], then she is not lawful to him afterward until she marries another husband." She does not become lawful for her first husband again until she enters into a valid marriage with another man who consummates the marriage with her, and then divorces her. Furthermore, the second marriage must be intended to be permanent, not merely to make her lawful for the first husband. Indeed, both the one who makes her lawful (the muḥallil) and the one for whom she is made lawful are accursed.