What is the ruling regarding a vow to fast Mondays and Thursdays for life for someone who made such a vow but is no longer able to fulfill it due to old age and illness?

The scholars disliked conditional vows (al-Nadhir al-Mu'allaq), based on the Prophet's (peace be upon him) saying: "It is only extracted thereby from the stingy." However, a Muslim must fulfill a conditional vow if its condition is met, as Allah Almighty says: "And let them fulfill their vows," and the Prophet (peace be upon him) said: "Whoever vows to obey Allah, let him obey Him."

Therefore, if the woman vowed to fast Mondays and Thursdays for the rest of her life and the condition of her vow is met, she must fulfill it, unless she becomes permanently unable, in which case she must offer the expiation for an oath (kaffarat yamin). If the condition of the vow is not met, then nothing is required of her.

It is a condition for a vow to be binding that it be in a form that implies commitment, such as "For Allah is upon me that I do such and such." As for merely saying, "If such and such happens, I will fast," it is not considered a binding vow.