Can you post photos? Persimmons are susceptible to Verticillium wilt, a soil pathogen that can prove fatal to a vast number of plant species.

I'll try; I'm not technically up-to-date, so let's see if this works.

Photos are there so good job with that :-) However, it would be more informative to see a photo of the entire tree taken from a distance.

I would still not be able to confirm whether or not Verticillium wilt was the problem but wilitng in sections or restricted to individual branches is very characteristic of the symptoms of this disease. The only way to confirm is to take one of the affected branches to your extention service office and have it evaluated by a plant pathologist.

OK here are some pictures of the tree.

yeah, that doesn't look too good :-( I'd certainly take a sample branch in for a diagnostic evaluation.