Is it permissible for a woman to remain with her husband who curses her, knowing that cursing is expulsion from God's mercy, and that this behavior is repeated by him?

There is no blame upon you for remaining with your husband, as cursing does not affect the validity of the marriage contract. However, it is dangerous and blameworthy in Islamic law, and it is not permissible for your husband to curse you or anyone else. If he curses unconsciously, then he is excused, and his words are considered idle talk. He must avoid the causes of anger, and you should avoid anything that provokes his anger.