The Sages enacted two Habdala recitations on Mosa’eh Shabbat. The first is the recitation of "Ata Honantanu" in Arbit, which speaks of the theme of "distinction," that Hashem distinguishes between day and night, between the Jews and the other nations, and between Shabbat and weekdays. The second is the Habdala recitation over a cup of wine after Arbit, which likewise speaks of these distinctions.
The Sages instituted the recitation of "Ata Honantanu" in the fourth Beracha of the Amida, the Beracha of "Ata Honen," in which we pray for wisdom and intelligence. Distinguishing between different entities, such as between Shabbat and weekdays, and between Am Yisrael and the other nations, requires a degree of intelligence, and so "Ata Honantanu" is relevant to the section of the Amida in which we ask for intelligence. Additionally, as the Yerushalmi explains, it is inappropriate to ask for our needs on Shabbat, and so before we ask for our needs in the Amida prayer on Mosa’eh Shabbat, we must first recite Habdala to end Shabbat. As such, the recitation of "Ata Honantanu" was instituted in "Ata Honantanu," the first Beracha of the Amida in which we make requests.
As a general rule, one who forgets to recite "Ata Honantanu" in the Amida on Mosa’eh Shabbat does not repeat the Amida, since he in any event will be reciting Habdala over a cup of wine. There are, however, two exceptions to this rule. First, as the Shulhan Aruch writes, if a person forgot "Ata Honantanu" and then ate before reciting Habdala, he must then pray Arbit with "Ata Honantanu." Since he made two mistakes – omitting "Ata Honantanu" and eating before Habdala – he is penalized by being required to repeat the Amida. The second exception, which is noted by the Hesed La’alafim (Rav Eliezer Papo, 1786-1827), is one who knows he will not have access to wine for Habdala. Such a person who forgets "Ata Honantanu" in Arbit must repeat the Amida so he can recite "Ata Honantanu," since this is the only Habdala he will be able to recite.
Summary: One who forgets "Ata Honantanu" in Arbit on Mosa’eh Shabbat does not repeat the Amida unless he knows he will not have access to wine for Habdala, or if he then eats before reciting Habdala.
