After Yom Tob, a person is required to recite Habdala over a cup of wine, just as one does after the conclusion of Shabbat every Saturday night (see Shulhan Aruch, Orah Haim 491:1). Unlike after Shabbat, however, after Yom Tob one does not recite the Beracha over the spices ("Besamim") or the Beracha over fire ("Boreh Me'oreh Ha'esh"); he recites only "Boreh Peri Ha'gefen" and the Beracha of "Ha'mabdil." This obligation applies both after the first days of Yom Tob, with the onset of Hol Ha'mo'ed, as well as on the conclusion of the final day of Yom Tob.
If a person did not, for whatever reason, recite Habdala on the night after Yom Tob, should he recite it at some later point, or does Halacha allow reciting Habdala only on that night?
With regard to Habdala after Shabbat, the Shulhan Aruch (299:6) cites two views as to the "deadline" before which this Habdala must be recited. One view maintains that one may recite Habdala through Sunday; according to this view, a person who did not recite Habdala after Shabbat until Sunday night may no longer do so. The second view, by contrast, contends that one still has the opportunity to recite Habdala until Tuesday. Hacham Ovadia Yosef ruled that one may recite Habdala only until the end of the day on Sunday, and only if he had not yet eaten since the conclusion of Shabbat. Once a person eats after Shabbat, or once the day ends on Sunday, one can no longer recite Habdala.
With regard to Habdala after Yom Tob, too, we find different views. Rabbi Yehuda Aya'ash (Algeria, 18th century), in his work Bet Yehuda (2:28), rules that one has the opportunity to recite Habdala throughout the week following the festival. So long as a week has yet to pass since the conclusion of Yom Tob, one may still recite Habdala.
Many others, however, disputed this position, and held that one may not recite Habdala at any point beyond the night following the conclusion of Yom Tob. The Hida (Rav Haim Yosef David Azulai, 1724-1806), both in Birkeh Yosef and Mahazik Beracha, writes that one should not rely on this ruling of the Bet Yehuda. This stringent view is followed by the work Zera Emet (by Rabbi Yishmael Ha'kohen of Modona, Italy, 18th century), as well. The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) codifies this position in Parashat Vayeseh (Shana Sheniya, 23). More recently, Hacham Ben Sion Abba Shaul accepted this ruling in his work Or Le'sion (vol. 3, p. 197).
The Shulhan Aruch makes no mention of this case, which led many later authorities to conclude that he followed the second view recorded above. He likely held that Habdala may not be recited beyond the night after Yom Tob, and he therefore simply stated the requirement to recite Habdala on that night, without mentioning any possibility of reciting it at some point thereafter. This is indeed the accepted Halacha.
Summary: One who did not, for whatever reason, recite Habdala during the first night after Yom Tob, may no longer recite Habdala.
