I don't usually see it but there was one behind our house for several years, it was a bit crowded by the oaks. Then a couple years ago it dropped all its leaves early, all of a sudden, and when nothing grew back the next spring I cut it down. Now there are persimmon logs lying back there.
Other persimmons seem to do fine though. I've seen some for years that are still the same...except maybe a little extra girth.