R’ Akiva Eiger (Shut”T siman 1) writes that women are allowed to fast on Yom Tov because the mitzvah to eat on Yom Tov is an extension of the halacha of oneg, which is a mitzvas aseh she’hazman gerama. The same holds true of the mitzvah of simcha. According to many Rishonim the mitzvah of simcha is incumbent upon a husband to make his wife happy, but there is no chiyuv of simcha that applies directly to women (Ra’avad Hil Chagiga 1:1, see Rambam and meforshim there). Therefore, a women who forgets ya’aleh v’yavo in her bentching need not repeat birchas hamazon.
Rav Zolti in his discussion of simcha on Purim makes a beautiful point. There is no one who suggests that a women should observe aveilus on Yom Tov, despite the fact that they have no chiyuv of simcha. Yet, wouldn’t this be the logical outgrowth of R’ Akiva Eiger’s chiddush?
The reason aveilus does not apply to women, explains R’ Zolti, is because it's not the kiyum mitzvah of simcha by the individual which is doche aveilus [it’s not an aseh doche lo ta’aseh halacha], but rather it is the characters of the day of Yom Tov itself as a day of simcha which blocks aveilus [the day is mufka from aveilus]. Women may be exempt from kiyumei mitzvah of simcha, but that does not change the nature of the day. For the same reason, women must repeat birchas hamazon of they forget ya'aleh v'yavo.
Support for this conclusion comes from the Rambam:
שבעת ימי הפסח ושמונת ימי החג עם שאר ימים טובים, כולם אסורים בספד ותענית. וחייב אדם להיות בהן שמח וטוב לב, הוא ובניו ואשתו ובני ביתו וכל הנלווים עליו, שנאמר "ושמחת, בחגך . . ."
The Rambam prefaces the obligation of simcha on Yom Tov with the halacha that mourning is prohibited. Isn't that that putting the cart before the horse? It’s the obligation of simcha which is what deflects mourning; shouldn't it therefore be mentioned first?
The answer is that the Rambam is describing two different obligations: 1) the chovas hagavra of simcha; 2) simcha which is part of the character of the day itself. The Rambam begins by telling us mourning is suspended; the day itself has a certain character. The Rambam then follows with a detailed explanation of what an individual must do to reflect that character in tangible kiyum mitzvah behavior.