אורח חיים קכ״טOrach Chayim 129

Se’if 1א׳

אֵין נְשִׂיאַת כַּפַּיִם אֶלָּא בְּשַׁחֲרִית וּמוּסָף וּבִנְעִילָה, בְּיוֹם שֶׁיֵּשׁ בּוֹ נְעִילָה כְּמוֹ בְּיוֹם הַכִּפּוּרִים, אֲבָל לֹא בְּמִנְחָה, מִשּׁוּם דִּשְׁכִיחָא שִׁכְרוּת בְּאוֹתָהּ שָׁעָה, שֶׁמָּא יְהֵא הַכֹּהֵן שִׁכּוֹר; וְגָזְרוּ בְּמִנְחָה שֶׁל תַּעֲנִית, אָטוּ מִנְחַת שְׁאָר יָמִים; אֲבָל בְּתַעֲנִית שֶׁאֵין בּוֹ נְעִילָה, הוֹאִיל וּתְפִלַּת מִנְחָה סָמוּךְ לִשְׁקִיעַת הַחַמָּה, הִיא דּוֹמָה לִתְפִלַּת נְעִילָה וְאֵינָהּ מִתְחַלֶּפֶת בְּמִנְחָה שֶׁל שְׁאָר יָמִים, הִלְכָּךְ יֵשׁ בָּהּ נְשִׂיאַת כַּפַּיִם. וְהַמִּנְהָג שֶׁלָּנוּ כְּבַר נִתְבָּאֵר לְעֵיל סי' קכ"ח.

During Which Services We Lift the Hands [Perform the Priestly Blessing], Containing 2 S'ifim: We only lift the hands [perform the Priestly Blessing] during Shacharit and Mussaf, as well as during N'ilah on a day that has N'ilah, such as Yom Kippur; but not during Mincha, since it is drinking [alcohol] is likely [by] that time, and perhaps the Kohen would be drunk. They decreed [similarly regarding] during Mincha on a fast day because of Mincha on other days (i.e., lest people come to think that Birkat Kohanim during a regular Mincha is permitted). But on a fast day that does not have N'ilah, since the Mincha prayers are said close to [the time of] the setting of the sun, it's similar to the N'ilah prayers and will not be confused with Mincha on other days, therefore they do perform Birkat Kohanim. And our custom has already been explained above in Siman 128.

Se’if 2ב׳

כֹּהֵן שֶׁעָבַר וְעָלָה לַדּוּכָן בְּיוֹם הַכִּפּוּרִים בְּמִנְחָה, כֵּיוָן שֶׁהַדָּבָר יָדוּעַ שֶׁאֵין שָׁם שִׁכְרוּת, הֲרֵי זֶה נוֹשֵׂא אֶת כַּפָּיו וְאֵין מוֹרִידִין אוֹתוֹ, מִפְּנֵי הַחֲשָׁד, שֶׁלֹּא יֹאמְרוּ: פָּסוּל הוּא וּלְכָךְ הוֹרִידוּהוּ. הַגָּה: וְלָכֵן אוֹמְרִים בְּמִנְחָה בְּיוֹם כְּפוּרִים: אֱלֹהֵינוּ וֵאלֹהֵי אֲבוֹתֵינוּ, אַף עַל גַּב דְּאֵין רָאוּי לִנְשִׂיאַת כַּפַּיִם, מִכָּל מָקוֹם הוֹאִיל וְאִם עָלָה לֹא יֵרֵד מִקְרֵי קְצָת רָאוּי (הַגָּהוֹת מַיְמוֹנִי), וְכֵן נוֹהֲגִין בִּמְדִינוֹת אֵלּוּ אַף עַל פִּי שֶׁיֵּשׁ חוֹלְקִים.

A Kohen who transgressed and went up to the platform [to perform Birkat Kohanim] on Yom Kippur during Mincha - since it's known that no one is drunk then, he may lift his hands [to perform Birkat Kohanim], and they [the congregation] may not bring him down because of any suspicion - in that people shouldn't say that he was unfit [to perform Birkat Kohanim] and that's why they brought him done. Gloss: Therefore, during Mincha on Yom Kippur, they say "Our G-d, and the G-d of our Forefathers...", even though it's not a time that's fitting to perform the lifting of the hands; nevertheless, since if [a Kohen] did go up, he does not come down, it's considered to be somewhat of a fitting time (Hagahot Maimoni). And such is what we practice in these lands, even though there are some who disagree.