During the Amida prayer and Birkat Hamazon on Rosh Hodesh, one must add the paragraph of "Ya’aleh Ve’yabo." One who forgot to add "Ya’aleh Ve’yabo" in the Amida of Shaharit or Minha on Rosh Hodesh must repeat the Amida. At Arbit of Rosh Hodesh, however, one who forgets to recite "Ya’aleh Ve’yabo" does not repeat the Amida. This applies even on the second night of a two-day Rosh Hodesh.
Must one repeat Birkat Hamazon on Rosh Hodesh if he forgot to add "Ya’aleh Ve’yabo"?
The Shulhan Aruch (Orah Haim 188:7) rules that if the person realized his mistake immediately after completing the Beracha of "Boneh Yerushalayim," then he should recite the phrase, "Baruch She’natan Rosheh Hodashim Le’amo Yisrael Le’zikaron." This phrase is recited without the words "Hashem Elokenu Melech Ha’olam," and the text appears in many editions of the Siddur.
If a person did not realize his mistake until after he recited Hashem’s Name in the next Beracha (the Beracha of "Ha’Kel Abinu Ro’enu"), then he simply continues Birkat Ha’mazon without reciting Ya’aleh Ve’yabo. One cannot add Ya’aleh Ve’yabo in the "Harahaman" section of Birkat Hamazon.
If one realized his mistake after he began the phrase, "Ve'tibne yerushalayim," before reciting Hashem’s Name in the Beracha, then he recites "Ya’aleh Ve’yabo" and then proceeds as usual with "Ve'tibne yerushalayim." If he realized his mistake after he recited Hashem’s Name in the Beracha, but before he recited the words "Boneh Yerushalayim," then he should recite the words, "Lamedeni Hukecha" so that he will have recited a complete verse ("Baruch Ata Hashem Lamedeni Hukecha" – Tehillim 119:12), and will thus not have recited Hashem’s Name in vain. He should then recite "Ya’aleh Ve’yabo" and proceed as usual with "Ve'tibne yerushalayim."
These Halachot apply throughout Rosh Hodesh, both by day and by night.
Summary: One who forgets to add "Ya’aleh Ve’yabo" in the Amida on Rosh Hodesh during Arbit does not repeat the Amida; if this occurred during Shaharit or Minha, he must repeat the Amida. If one forgot to recite "Ya’aleh Ve’yabo" on Rosh Hodesh in Birkat Hamazon, and did not realize his mistake until after he recited Hashem’s Name in the Beracha of "Ha’Kel Abinu," he continues as usual and does not recite "Ya’aleh Ve’yabo." If he remembered after the Beracha of "Boneh Yerushalayim," but before the Beracha of "Ha’Kel Abinu," then he should recite the phrase, "Baruch She’natan Rosheh Hodashim Le’amo Yisrael Le’zikaron." If he realized his mistake before he recited Hashem’s Name in the Beracha of "Boneh Yerushalayim," then he recites "Ya’aleh Ve’yabo" and then proceeds as usual with "Ve'tibne yerushalayim."
