If a woman broke her fast in Ramadan with a valid excuse, is it obligatory for her to make up for the days that she missed consecutively or can she do that separately, according to her ability?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Muslim scholars have two different views on this issue:

First, if a person breaks his fast on consecutive days in Ramadan, such as when a woman breaks her fast because of menstruation, then one must make up for these days consecutively.

Second, consecutiveness is not required for the validity of making up for missed Ramadan fasts, as indicated by the Saying of Allah (which means): {So whoever among you is ill or on a journey [during them] - then an equal number of days [are to be made up].} [Quran 2:184]

However, observing consecutiveness when making up missed Ramadan fasts is highly recommended as one might die before completing the set of days that he is required to make up for. This second view is the preponderant one since the aforementioned verse makes no mention of consecutiveness as a condition for the validity of the fasts.

The second view was also adopted by some companions of the Prophet including Abu ‘Ubaydah ‘Aamir ibn Al-Jarraah, Ibn ‘Abbas, Abu Hurayrah, Mu‘aath ibn Jabal, and ‘Amr ibn Al-‘Aas all. This is also the view adopted by the majority of the Muslim scholars. In his book of Tafseer, Al-Qurtubi says, “The majority of Muslim jurists hold the view that making up for the missed days of Ramadan in succession is recommended. However, doing this on separate days clears one of his liability.” The evidence to support this view is the Saying of Allah (which means): {... then an equal number of days [are to be made up].} [Quran 2:184]
Allah Almighty does not specify such days as being consecutive or separate. Hence, if the person fasts on separated days, he will actually have fasted 'an equal number of days', as stated by the verse. Therefore, this will be sufficient for fulfilling the duty.

Ibn Al-‘Arabi, says: “Consecutiveness is obligatory in fasting the month of Ramadan owing to the fact that such a month is specified by Allah as the month of fasting. However, there is no specification for the days on which one is required to make up for missed days of Ramadan fasts, so doing this on separated days is allowed.”

Allah Knows best.