Joe *spoilers*
I saw this movie when it first came on HBO. I guess that was nearly 7 or 8 years ago? I rewatched it for the first time in years today, and I came to the conclusion (that I hadn't before) that Joe had killed himself by 1990.
He was broken, he was really weak to begin with, he was struggling with his personal and moral and sexual identity. His wife left him, and so did Louis. Most telling of all was the very end of the movie when Hanna, Louis, Belize, and Prior are all talking by the fountain. There was something about how different Hanna was and how Joe wasn't there that sort of led me to believe he might have killed himself after when we last saw him say good bye to her by the group of singing people.