The Shulchan Aruch notes that a priest who is in mourning for one of the seven close relatives does not bless the people during the Shiva period. The Rama extends this and says that a priest who has lost a parent should not duchen for the full year extended period of mourning. (See Orach Chaim 128:43, and see paragraph 44 regarding the requirement that the priest must be b’simchah, in a joyous mood, to participate in Bircas Kohanim.) Had Bircas Kohanim been a mitzvah of simple recitation of some text, it should have been treated the same as tefillah and Keriyas Shema, which are mitzvos that the mourner must fulfill despite his depressed frame of mind. Apparently the requirement to perform Bircas Kohanim with love prevents the kohen mourner from going up to bless the people.
The Rama (ibid) rules that in the diaspora, the kohanim do not perform Bircas Kohanim daily because they are preoccupied with thoughts of daily survival and the need to earn a living, [which precludes them from fulfilling their obligation with its proper intent]. We do not find that similar pre-occupation removes the obligation to recite Keriyas Shema or to pray on a daily basis. The word amor teaches that there is a biblical obligation to perform this mitzvah, b’ahavah, which is different than other mitzvos. The fulfillment of b’ahavah requires the priests to bless the people with the proper intent and with a full heart, and not to bless them in a hasty or perfunctory manner or in a bewildered mood. This precludes Bircas Kohanim on a daily basis in the diaspora. However on festivals that are associated with joy and simchah, the obligation to bless the people applies in the diaspora as well. The Rama notes that the blessing should be done in Mussaf, in closest proximity to the end of the service so as to connect it with the joy and simchah of the holiday felt by the people (perhaps in connection with the se’udas Yom Tov after tefillas Mussaf).
In summary, the perpetual obligation to bless the people indicated by amor (similar to zachor) is connected to the obligation to bless them b’ahavah. Amor teaches that the kohen must always be ready to bless the people based on this perpetual obligation, just like the Jew must always think of Shabbos. Amor also teaches that it must be done through ahavah, that this perpetual obligation can only be fulfilled when the kohen is of a clear frame of mind.