بسم الله الرحمن الرحيم
If by keeping fast in Ramadan the mother has not to experience any problem in breastfeeding her child and the child will not meet any harm then it is mandatory for the mother to observe the fasts. But in case of keeping fast if there is fear of life then the mother should not keep fast rather she can postpone.
Allah knows Best!
Darul Uloom Deoband
This answer was collected from the official ifta website of Darul Uloom Deoband in India.