His girlfriend was always bucking him up with her words, but she ran out of patience with him and left him.
この場合、次のような言い方ができますよ。
ーHis girlfriend was always bucking him up with her words, but she ran out of patience with him and left him.
「彼女はいつも彼のことを励ましていたが、彼に愛想を尽かして出て行った」
to buck someone up with one's words で「言葉で人を励ます」
to run out of patience で「愛想を尽かす」
ご参考まで！
カナダ 
