From: Rabbi Akiva Eiger
To: Rabbi Leib
Rabbi Akiva Eiger affirms that men who forget Ya'aleh VeYavo in Birkas HaMazon on Yom Tov must repeat, distinguishing Yom Tov (obligatory bread meal) from Rosh Chodesh (no such obligation). He adds a novel ruling that women need not repeat, as they may be exempt from oneg Yom Tov as a time-bound positive commandment — with exceptions for the first night of Pesach (matzah obligation via hekesh) and Shabbos (equated to men via zachor/shamor).
Source: Shu"t Rabbi Akiva Eiger §1