The Shulhan Aruch (Orah Haim 126) rules that if a Hazan forgot to include Ya’aleh Ve’yabo during the repetition of the Amida during Shaharit on Rosh Hodesh, and nobody realizes this omission until he completed the repetition, then he does not need to repeat the Amida a second time. Since the Hazan will soon be reciting the special Musaf prayer for Rosh Hodesh, this suffices after the fact, given the importance of not inconveniencing the congregation by having the Hazan repeat the Amida again.
The question arises as to whether this applies also if the Hazan forgot to include Ya’aleh Ve’yabo during Minha on Rosh Hodesh. If this occurred on the only day of Rosh Hodesh, or on the second day of Rosh Hodesh, then undoubtedly, the Hazan needs to repeat the Amida, because no other Rosh Hodesh prayer remains. However, if this occurred during Minha on the first day of Rosh Hodesh, we might assume that the Hazan can rely on the fact that he will be reciting Ya’aleh Ve’yabo during Arbit that night. Just as we can rely on the Musaf prayer when the Hazan forgot Ya’aleh Ve’yabo during Shaharit, in order not to inconvenience the congregation, perhaps we can likewise rely on the evening Arbit prayer if the Hazan forgot Ya’aleh Ve’yabo during Minha. On the other hand, one might distinguish between the two cases, in light of the fact that the new Halachic day begins at night, such that the Arbit prayer is recited on a different Halachic day. Therefore, if the Hazan forgot to include Ya’aleh Ve’yabo during Minha even on the first day of Rosh Hodesh, perhaps he must repeat the Amida again, because the nighttime Arbit prayer belongs to a different day and thus cannot suffice to substitute for the missed Ya’aleh Ve’yabo recitation during Minha.
Hacham David Yosef, in his Halacha Berura, brings different opinions on this matter, and leaves this question unresolved. As mentioned, however, it is clear that if this occurred during Minha on a one-day Rosh Hodesh, or on the second day of Rosh Hodesh, then the Hazan will certainly need to repeat the Amida a second time.
Incidentally, it is worth noting a somewhat similar Halacha regarding the Friday night Arbit service. If the Hazan mistakenly recited the weekday Amida on Friday night instead of the special Amida for Shabbat, then he may rely on the "Me’en Shalosh" text recited after the Amida ("Magen Abot…"). This text summarizes the Amida, and so its recitation can count as the Hazan’s Amida in order to avoid the inconvenience to the congregation if they would have to wait for the Hazan to recite the correct Amida.
Summary: If the Hazan forgot to include Ya’aleh Ve’yabo during the repetition of the Amida in Shaharit on Rosh Hodesh, and nobody realizes this omission until he completed the repetition, then he does not need to repeat the Amida a second time. If this occurs at Minha on a one-day Rosh Hodesh, or on the second day of a two-day Rosh Hodesh, then the Hazan must repeat the Amida again. If this occurs at Minha on the first day of a two-day Rosh Hodesh, it is uncertain whether the Hazan must repeat the Amida again.
