There is not a lot of information in the photo to support a diagnosis, but what I can't see could be a contributor. I can't see the root flare. If the little fella was planted too deeply, innocuous as it seems, the consequences could be dire, but it's fixable. It is not unusual for young trees to be planted too deeply by growers, shipped to nurseries and sold that way. The end user has a chance to correct the problem, as long as they know there is one. It usually takes years before the final price is paid.
Tve photographs bellos depict two trees with different fates awaiting them. The first one shows a tree that resembles a phone pole. The tree is doomed. The second is a properly planted tree. (Three other ideas about your fuyu follow the photos.).
I believe you said a nursery worker told you that persimmons resist Armillaria root rot. They might, but they are not completely insusceptible. One must always consider the source of such information. (I asked about some barely detectable insects crawling in and out of the bark of a weeping willow I had just bought when two nursery workers were loading it onto my vehicle. They said it was no big deal, so I swapped it on the spot for a climate-suitable tree. Since then, wised up, I have not seen a weeping willow in my subtropical climate that didn't show a little bit of sparseness of foliage at the very top of the tree. I amaze my friends by accurately pronouncing "two years from now, that tree won't be there." About the persimmon, though. I have come across the claim that they are Armillaria-resistant, but I have seen more convincing writings on how to deal with it should it occur. One article said to kill all your trees and start over. Another said phosphorous acid can keep it in check. Mainly, for now, don't rule it out. If that's what it is, there might be some options.
Another possibility, among many, is phytopthora, a very common disease that persimmons are susceptible to. The pathogen is a weird little thing called an oomycete. (It isn't a fungus, a bacterium or a virus. It's an oomycete.) Your tree doesn't show any of the problems that phytopthora causes, but the disease does its damage in the roots, and the symptoms appear above the soil later. I've had a crash course this year, with a gorgeous young avocado that had bloomed for the first time and set what seemed like a thousand tiny fruit. They grew to the size of kumquat and stopped, and hung around looking pathetic while the tree underwent two vigorous leafings-out that resulted in masses of ugly yellow leaves that soon developed dry brown splotches that made them as ugly as arborily possible. I don't know why that pathogen was in my soil. I do know what I and two well-meaning others did wrong, though.
I was thrilled to learn that it is controllable, and possibly even curable. I bought a few slow-release tree injectors from the US distributor, some buffered phosphorous, not phosphoric, acid made by Monterey Lawn and Garden, sold as GardenFos by the company and lots if other online retailers. The tree soon had shed its ugly yellow-brown adornments and very promising new leaves have emerged. It might need additional injections, but I wouldn't resume until next year, if that's so.
- One more thing. Sometimes what seems to be a sick tree is just a species with unusual scheduling . This article...
...on SFGate.com lists some benign explanations for troubling phenomena in persimmon trees.
The last part of the last thing: If you're in Australia or anywhere in the southern latitudes, it's winter, persimmons are deciduous.