Well, since no one here had a suggestion, I bit the bullet (Felcos?) and cut down the bald branches. No green inside (whew!). But there are other branches from the same plant with all their leaves, just beginning to fruit.
I'm guessing it was either some sort of disease or the cycle of the plant--after a few years of blooms, it's time to prune off branches that lose their leaves.

I have a few growing naturally at the edge of the woods. They look nice when flowering, but then get a black mildew in the summer and lose a few leaves.

Yes, branch dieback will be the result of a problem.

What sort of problem? It hasn't affected other branches. The dieback went all the way to the trunk of the plant.