Does it look like a Fungal disease or root rot?

Does the curling or wilting continue to happen? How does the tree look now?

It's worsened a lot. It's on a few more branches now.

Can we see new photos? And ones that clearly illustrate the issues?

Okay, here's photo's:

So it is essentially one entire branch that has wilted and dried? That's not a good sign and could indicate a serious problem. But if it is what I think it may be (Verticillium wilt) there's not a dang thing you can do about it anyway. Just keep an eye on it for now. If the entire tree develops the same symptoms, you may have lost it. But sometimes a branch will wilt independent of the rest and the tree will survive. You won't really know until it leafs out - or doesn't - in spring and I wouldn't cut it off until then.

Thanks for the info. There's at least 4 separate branches that have wilted.

Update. It's much worse now.