They do seem a bit spindelly for 3 years. The first year after planting is critical for watering during dry spells for good root development and applying some 10-10-10 fert a bit around the perimeter each Spring to give it a boost. If you've been doing that it should be ok. Keeping the soil clear of weeds around the base helps a lot. The first pic shows dead wood? if the wood/stems are not green inside that dead wood could be pruned away down to any new growth/sprouts. Those base sprouts may be from the root graft and if so should be removed. Does it get fun sun? Mine is about 15 years old now and gets all day full sun, about 8-10 hours.

^^^ It's an Ichi Ki Kei Jiro non-astringent variety.

The one tree looks like a perfectly normal, healthy persimmon to me, and the regrowth from the other tree does, too. I don't have any ideas why the graft would have died, though.