Is it permissible for a mother to continue fasting all days of the week—except for Friday and sometimes Saturday or Sunday—given that she works as a teacher and experiences great fatigue, and in a city where the Maghrib adhan is delayed until 8:30 PM, or is it better for her to limit her fasting to Mondays, Thursdays, and the White Days?

If your mother's fasting most days of the week does not harm her and does not prevent her from fulfilling her religious obligations, then there is no sin upon her; rather, she is upon great good. Her fasting is not considered the perpetual fasting that is forbidden, as long as she breaks her fast on some days of the week.

Imam An-Nawawi stated that the ruling on perpetual fasting is that it is disliked if one fears harm or the neglect of a right. If one does not fear harm and does not neglect a right, then it is not disliked. This is what Ash-Shafi'i and the majority of scholars stipulated. An-Nawawi mentioned that many of the Salaf (early Muslims) and Khalaf (later Muslims) fasted perpetually, with the exception of the days when fasting is forbidden.

The fact that her fasting prevents you from enjoying her company is not a justification for ordering her to break her fast. You can enjoy her company after she breaks her fast or on the days when she is not fasting.