Praise be to Allah.
It should be pointed out that making vows is makrooh or haraam, because it obliges the Muslim to do something that he may not be able to do, or it may be very difficult for him to do when he is fine without it.
The Muslim should do good deeds, such as fasting and other acts, without making vows, when he has the option of not doing it if he so wishes. But if he makes a vow, he is obliging himself and making it obligatory to fulfil his vow, if it is a vow to do an act of obedience, because the Prophet (blessings and peace of Allah be upon him) said: “Whoever makes a vow to do an act of obedience to Allah, let him do it”; and he (blessings and peace of Allah be upon him) said: “Fulfil your vows.” And Allah, may He be exalted, says (interpretation of the meaning) “They (are those who) fulfill (their) vows” [al-Insaan 76:7]; “Then let them … perform their vows” [al-Hajj 22:29]; “And whatever you spend for spendings (e.g., in Sadaqah - charity, etc. for Allahs Cause) or whatever vow you make, be sure Allah knows it all” [al-Baqarah 2:270].
If a person does make a vow, and it is a vow to do an act of obedience, then he is obliged to act upon it, but if he has not already made a vow, the Muslim should not oblige himself or make a vow.
What the questioner mentions, about having made a vow to fast the first nine days of Dhu’l-Hijjah on a permanent basis, is a vow to do an act of obedience and she is obliged to fulfil it. Her husband does not have the right to prevent her from doing that, because her husband may only prevent her from observing voluntary fasts. But in the case of obligatory fasts that are connected to a specific time, it is not permissible for her husband to prevent her from doing it. She made a vow to fast these specific days, so she must fulfil that vow. If she says that she is not able to do it for health reasons, if what she means is that it is difficult for her, that does not mean that she should not do what has become obligatory, even if it is difficult for her; so she should fast, because she has obliged herself to do that. It is well-known that fasting may be difficult even for one who is strong.
But if what she means is that she cannot fast, then in the year in which she is not able to fast because of sickness or physical weakness, she must offer expiation for breaking an oath (kafaarat yameen). Then if she becomes stronger in the following year, she must fast, and so on.
Therefore it is not permissible for her to not do what she vowed to do, because she has obliged herself to do that. The Muslim should not take the matter of vows lightly, making a vow and obliging himself to do something, then after that looking for ways out and tricks to avoid doing it. This is not permissible, because what one vows to do becomes an obligatory duty, and it is not permissible to not do it without a legitimate shar‘i reason.
If those days coincide with her monthly period, then she is excused for not fasting them, because this is a legitimate shar‘i excuse, such as if she falls sick. This excuse waives the obligation of fasting on those days, but if those days come and she has no legitimate shar‘i excuse, in the sense that she is in good health and is not menstruating, then she must fast them.