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Rema (Orach Chaim 128:44) says that since the point of the Ashkenazic custom to limit Birkas Kohanim to Yom Tov is so that the blessing should be given in a joyous frame of mind, then it is done only at Musaf, since then people are especially happy at the impending prospect of the Yom Tov meal.
(Yom Kippur, of course, is the exception. I believe there are indeed Ashkenazic congregations that have Birkas Kohanim at Ne'ilah as well, provided of course that it's not too late in the day. Not sure about Minchah.)