Sorry to say, burning bush does that sometimes - a branch or two will simply up and die mid-season. Not a bacterial blight - it does happen to leaves still growing but they do not blacken and die instantly (as we say of blight "it looks like the wicked witch of the west just zapped them). Instead, the leaves go through color change like you describe, then do not fall but end up brown and dry. Sometimes the next year the whole bush just goes, the same way, mid-season.
A fungus that gets into the wood seems to be responsible: Sclerotinia sclerotiorum. (It's sometimes called "White mold", but the appearance that gave it that name is more likely to occur inside tissues when it infects flowers and stems of the hundreds of non-woody plants it can infect.) Sometimes just the couple of branches die back. We used to say dieback from this fungus was closely linked to drought years, perhaps because it is best able to kill already-weakened wood. However, for the soft-tissued plants it affects, 10 days of cool wet weather seems to open the door to infection.
More on this disease at https://ipm.illinois...s/rpds/1008.pdf
Since this fungus is most prevalent on herbaceous (soft) plants, much of this very informative bulletin deals with handling the disease or agricultural and floral crops.
Prune out the dead wood looking for discolored wood and bark to be sure you cut below all the infected area. Sterilize your saw or loppers after the cut - use bleach or peroxide. If it is a very important plant you may want to follow up next year with a fungicide on the newly-forming leaves and new twigs, since this is when the fungus first invades the wood, when it is new and green.
Sorry to be giving you such a delayed response. We've fallen behind this year. Pandemic lockdown delayed all our April work and we gardeners know April will NOT be held back. So catching up April meant running like heck all May and June to compensate. Now we are mostly back on track outside but most of our administration time has been and still is being taken up by Forum work you do NOT see. We are getting a much needed upgrade and reprogramming to make the Forum simpler to use from cell phones, easier to join, and better able to repel ad-bots. (We spend time every single day kicking out ad-bots that made it partway through to becoming members. Most would fail then and never get past that point but some would get through the last defenses - it's all a numbers game, bots trying out combination after combination to break security codes. So we kick them out at failsafe #1.) Anyway, we are back now, catching up and enjoying this!