The Gemara here tells us that Sarah, Rachel and Chanah were blessed with children on Rosh Hahsanah ("Nifkedah").
What does this mean - don't we know that the mal'achim came to Abraham on pesach and Sarah gave birth one year later on pesach -- not rosh hashanah!
Yehoash Orange
Rashi in Rosh Hashanah 11a explains this statement to mean that on Rosh Hashanah, these Tzidkaniyos were declared before Hash-m as fit for having children and it was decreed that they would become pregnant that year.
Although it is possible to change one's fate through prayer during the rest of the year as well (see Tosfos Rosh Hashanah 16a DH k'Man), these Tzidkaniyos prayed for children on Rosh Hashanah (see Taz OC 597:1), during which it is more likely for Tefilos to be answered, and their Tefilos were indeed answered.
Best wishes,
Mordecai Kornfeld