According to the majority of scholars, including the Hanbali, Maliki, and Shafi’i schools, missed Ramadan fasts must be made up before the next Ramadan, as explained in the question about when should we make up missed Ramadan fasts. However, they differentiate between someone who delays making them up because of a valid reason and someone who delays without one.
If the delay is for a valid reason that prevents a woman from fasting back the days missed, such as sickness, pregnancy or breastfeeding, there is no sin on a person for delaying in this case, because she has an excuse, and she only has to make up for the days missed. She needs to make them up as soon as she is able to fast again, in addition to the days accumulated during the second Ramadan.
In the case where there is no reason for the delay, the person was able to make up the fasts but she did not do so before the beginning of the following Ramadan, this person is sinning by failing to make up the fasts with no excuse. The scholars agreed that she must make up the fasts, but they differed as to whether along with making up the fasts she must also give Fidya or not, which is feeding one poor person for each day.
Malik, al-Shafi'i, and Ibn Hanbal stated that the person needs to give Fidya, citing as evidence reports from some of the Sahabah, including Abu Hurayrah and Ibn 'Abbas (Radi'Allahu Anhuma).
Imam Abu Hanifah (Rahimahullah), however, believed that giving Fidya is not required in addition to making up the fasts. He supported this view by pointing out that in the Quran, Allah only commands the one who misses fasting in Ramadan to make up the fasts, without mentioning the need to feed a poor person.
In conclusion, women should be very careful to not delay fasts and ensure they make up for missed fasts before next Ramadan if there is no excuse. They should realize that otherwise they are committing a sin according to the majority of scholars, and they must repent to Allah and resolve not to repeat this mistake in the future. As for Fidya, if this situation occurs, despite the difference of opinion, given the fact that the majority of scholars saw that it should be given, it would be on the safe side to give it, and consider it as an action to repent for the sin.