You've just described my multi-grafted Northern Spy apple tree... It's Gravenstein branch is dying. With identical symptoms, I've no idea what's wrong? The rest of the tree looks normal. So, what to do?

It's hard to believe there's a pathogen on one limb that hasn't infected the remaining tree, so I'm in no hurry to remove it. Around the time fall burning season arrives I'll saw it off and burn it (or donate it to any friends who smoke fish or barbecue). I've read / learned that it's best to let the open wound dry and "heal" on its own - as opposed to sealing it with anything. I've noticed that a sealing / "healing" compound will trap moisture and allow rot; whereas letting it "heal" naturally looks to give the best results.

When you remove the limb, cut it off a foot or so away from the trunk (remember to first make a slight undercut a bit closer to the trunk than the final top cut - so it doesn't tear the bark as it falls). Make the finish-cut nearly flush with the tree trunk, but not too close, and never leave a stub.

Maybe Ted will tell us what caused our trees demise? I only hope it stops there, I've spent 3 years watching a tree entirely "consumed" by this slow death - this time I'd rather replace it sooner than later - so I'll be watching very closely next spring!