Siman 129

There is no nesiat kapayim except during Shacharit and Musaf, and Neilah on a day that has a Neilah prayer, such as Yom Kippur. And similarly on a communal fast during the time they used to practice praying the Neilah prayer, such as in the time of the Mishnah. But Minchah does not have nesiat kapayim because by Minchah all the people have already eaten, and perhaps the kohanim drank wine, and a drunkard is forbidden from nesiat kapayim. And even on a fast day they do not perform nesiat kapayim during Minchah, as a decree regarding Minchah of a communal fast on account of Minchah of every day.

To what do these words apply? To fasts in which they pray Mincha and Neilah. But a fast that does not have Neilah, such as Tisha B'Av, the seventeenth of Tammuz, and the tenth of Tevet, and likewise every communal fast among us, since their Mincha prayer is close to the setting of the sun—it appears like Neilah and is not confused with the Mincha of every day, and therefore it contains nesi'at kapayim. And a kohen who transgressed and ascended the duchen during Mincha of Yom Kippur, since it is a known matter that there is no drunkenness there—he performs nesi'at kapayim. And we do not remove him because of suspicion, so that they should not say he was unfit and therefore they removed him. So wrote the Rambam at the beginning of the fourteenth chapter of Tefillah, see there. And so wrote the Tur and the Shulchan Aruch. And in the name of the Bahag, the Tur wrote that on Yom Kippur they perform nesi'at kapayim during Mincha, because they increase supplications and it is also close to the sunset. And he wrote that in Ashkenaz they do not practice this, see there. And among us, in any case, aside from Musaf we do not perform nesi'at kapayim. (And from this it appears that they used to pray Mincha every day several hours before nightfall, because they wanted to eat after Mincha. So wrote the Magen Avraham, subsection 2, in the name of the Ran. And only on a fast would they pray close to the sunset.)

Our teacher, the Rema, wrote: Therefore, we say on Yom Kippur at Mincha "Our God... bless us..." even though it is not fit for the nesiat kapayim; nevertheless, since if he ascended he does not descend, it is called somewhat fit. And such is the custom in these lands, even though there are those who disagree. Thus far his words. And all the more so on every fast day that we say "Our God," for it is fit for nesiat kapayim. And our custom is that when we say "Our God," we say "Sim Shalom" and not "Shalom Rav." Nevertheless, those who fast until midday and afterwards pray Mincha Gedola—the custom is not to say "Our God," and they say "Shalom Rav." And even though according to the reason that if he ascended he does not descend it would be so then as well since they have not eaten and have not drunk, nevertheless, the custom is not so (see Magen Avraham, subsection 1).