Looks like they are still there because they have not ripened (unless the fruit from this tree does not mature orange or purple anyway). It also looks like it has been getting topped, hard pruning like this can result in a juvenile condition of outer branches due to them having sprouting in response to the damage. This could account for the persisting leaves even if it has nothing to due with the fruits still being green in November.

Yes. It's very common in November to have persimmons clinging to otherwise bare trees. In a week or so give the trunk a good shake and they'll come tumbling down.

Thanks Embothrium and HU. I have never topped this tree. I'll give it a good shake soon. :)