Answer
(Fatwa: 1077/1021=D/1429)
The vow (nazar) of your wife to keep fast for two days in a week is valid and she has to keep those fasts, but she is not bound to keep them on Saturday and Monday. If fast of any week is missed because of some excuses like illness, menses, then she has to do its qaza on any other day. But, if a fast is missed with no excuse, its qaza will also be necessary. Therefore, she should write it in a diary in which week she kept the fast and in which week she missed so that she can give fidya (expiation) or can do a will of giving fiday in case she becomes weak.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband