This is the work of some sort of borer. I have trouble with them getting into nursery stock, but they do not seem to bother the larger trees or limbs. When I first saw it, I thought it was an ambrosia beetle, but the ones I have had seem to be limited to one or two individuals to the plant (rootstock or young grafted plant). With ambrosia beetles, there is normally a lot of them attacking at the same time. There are several borers that affect persimmons and I have never know for sure which this one is.
http://insects.tamu.edu/fieldguide/bimg211.html
Ned