The Talmud states that even though omitting Ya’aleh V’Yavo from the amidah on Rosh Chodesh cause a need to repeat the amidah, this is not true in regard to Birkat HaMazon. This is due to the fact that a meal on Rosh Chodesh, while appropriate, is not mandatory. Therefore, on Shabbat and Yom Tov, when a meal is required omitting Ya’aleh V’Yavo [or R’tzeh] does require repeating Birkat HaMazon.

R. Akiva Eiger (Responsa, 1) observes that that last point would not always apply to women, as the obligation of Yom Tov meals is a mitzvat aseh she-ha-zman grama, and thus women are exempt. There would be no difference, then, between Rosh Chodesh and Yom Tov: fasting is prohibited but actual meals are not obligatory. He does note that exceptions would be the first night of Pesach, when women share the obligation of matzah, and Shabbat, as the obligation of three meals applies to men and women (see also Resp. Shevet HaLevi, IV, 18).

In regard to the first night of Pesach, some poskim (see Resp. Kinyan Torah B’Halakhah VII, 38:2, and Resp. Shraga HaMeir,VII, 117 and 118:1) raise the question of one who omits Ya’aleh V’Yavo and thus must recite Birkat HaMazon again, if a cup of wine must be used again. This question could be affected by at least two separate issues: a) does omitting Yaaleh V’Yavo completely invalidate the Birkat HaMazon, thus forcing its repetition to include all the requirements of the first one; or is it that the first Birkat HaMazon was valid, but a new one must be recited in order to provide an opportunity for Ya’aleh V’Yavo; b) is the requirement of four cups of wine on Pesach night an obligation to drink wine four times, which in this case is unaffected, or is it an obligation to recite all of the speech-oriented mitzvot of the night on a cup of wine (see Chiddushei Maran Riz HaLevi, Hil. Chametz U’Matzah), in which case a second recitation must again be done with the accompaniment of wine.