The Holy Prophet said:
Allah, the Mighty and Sublime, has waived fasting and half of the prayer for the traveler and for pregnant and breastfeeding women.
(Sunan an-Nasa’i, vol. 3, Book 22, Hadith 23,172)
If a mother is regularly nursing her child, she should not fast. If a mother is in the very last phase of nursing where she may only be nursing once at night, then this is a gray area. According to Fiqh, nursing in relation to fasting is categorized under illness. If an illness is further aggravated by fasting, then one should not fast even if the illness is as minor as a cold (Fatawa Hadrat Musleh Mau‘ud, vol. 1, p.167).
On the other hand, there are some long-term illnesses in which one does all work, such a person is not counted as ill and must fast (Fatawa Hadrat Musleh Mau‘ud, vol. 1, p. 168).
If an illness is not further aggravated or affected by fasting, then one should fast. If a mother is in the final phase of nursing where she is only nursing once a night, and she sees that nursing is not interfering with her fasting, then she can fast. Deciding to fast during the last phase of nursing is a decision to be made individually with taqwa.