I think it needs sun. Here's a site that might help. Take a good look at the picture of the bark. does that look like what you see on your tree?

Could it be possible that you have overwatered it? Do the roots have good drainage? The wild persimmons grow well where they are neglected.

Here is a link that might be useful: persimmon tree

Thanks for the advice and link. Mine is a Japanese persimmon (kaki?). The drainage is good. Seeing from the link that is is hardy through zone 10, I guess the full, all-day sun is not the problem.

That 'twist tie' might be the green grafting tape that some propagators use to wrap their grafts - and it does not degrade like most grafting rubbers; I've purchased plants with that stuff still in place, and it did, indeed girdle the plant, resulting in death and loss of the grafted variety. Cut it off/out.
Otherwise, the curled leaves may be an indication of persimmon psylla damage early in the season.

Here is a link that might be useful: Insect management in Asian persimmons