Generally speaking, persimmon drops fruit when a tree is young or it gets too much fertilizer especially nitrogen. Too much pampering is not good.

Some things that come to mind:

Certain varieties do need to be pollinated in order to bear a full crop though I couldn't tell you which ones they are. Commercial orchards sometimes do have some male trees interspersed among the bearing trees.

You say that the trees are getting enough water but are they getting watered frequently enough. You may try different watering patterns.

You may get some small improvement in yield if you apply some of the trace elements.