I thought it was made pretty clear at the end when he finally agrees to add the missing piece to his "repertoire" (LOL!) right before a very important saxophone performance. After he and Elaine finish and she tells him "you don't have to try so hard", he gets up there to give his performance and can't play at all.
"The Rye", incidentally, is one of my favorite episodes--I love it when Jerry steals that marble rye from Mrs. Choat--"Shaddup you old bag!" and Kramer feeding Rusty the horse that huge can of Beefarino from Price Club. Priceless!
I don't think I'll ever get tired of that show.
l2c