The first tshuvah in the Shu"t R' Akiva Eiger addresses the question of whether a woman who forgets ya'aleh v'yavo in bentching on Yom Tov must repeat her birchas hamazon. Omitting ya'aleh v'yavo on days where there is no obligation to eat bread, e.g. Rosh Chodesh, does not necessitate repeating bentching. R' Akiva Eiger writes that the obligation to eat a seudah on Yom Tov stems from the time dependent zman gerama mitzvah of kavod v'oneg, honoring Shabbos and Y"T, from which women are exempt. Since they do not have to eat a seudah of bread, women would not have to repeat bentching in this case.
Many achronim disagree with this entire approach of R' Akiva Eiger (a discussion for another time). R' Shlomo haKohen, the dayan of Vilna (Shu"T Binyan Shlomo vol II, O.C. 48), however writes that even if one accepts R' Akiva Eiger's premis, not all Yamim Tovim are alike. Chazal tell us (Pesachim 68) that even those Tanaim who otherwise allow fasting on Y"T agree that a seudah on Shavuos is obligatory as that is the "yom she'nitna bo Torah", the day the Torah was given, a day which requires celebration. Just like women are obligated in tefilah because the obligation stems from sevara, a logical argument (do women not need to beseech G-d for their needs?), here too, women are obligated in seudas Yom Tov on Shavuos because the source of the obligation is a logical argument (see Tosfor d"h haKol). Therefore, all would agree that a woman who forgets ya'aleh v'yavo on Shavuos must repeat her birchas hamazon.