Dang that's a big persimmon! I never see any that big around here. If it gives off fruit I'd say leave it. In my opinion the fruit would be worth way more when there are is plenty of other good wood out there. Also consider, how much wood that is. That's like an all day task cutting, splitting, and hauling a tree that size. And like someone else said cut when it warms and the juices start flowing a little bit in the tree so you can get that bark off nice and easy.