While these plants are generally trouble free, there are several diseases and pests that afflict Euonymus alatus  (burning bush) in this way.

Check the twigs to see if armored scale is present between the flanges. Check for any damage or unusual growth on the trunk of the plant. Look under the leaves for webs or insect eggs. If you notice any of these things, please get back in touch so we can discuss it. 

If the roots have been in standing water of excessively moist soil due to recent heavy rains, that can also cause rapid decline of this sort. Overly moist soil can also cause a twig blight that will cause defoliation after cankers appear on the twigs. It is also possible that your plant is suffering from anthracnose, a rain loving fungal disease.

If you do not find damage to the plant trunk or twigs, cankers or pests, please send a good photo of the leaves before they fall off, both sides, and we will see if a  disease is identifiable.

Thank you for the additional photos. The photo of the leaf shows that you may have some powdery mildew, which is difficult to control but also unlikely to cause the widespread damage that you are experiencing.

In the third photo, I believe that I can see many, tiny white spots on the plant stems. These could be either twospotted spider mites or winged euonymus scale insects, both of which could create the extreme die back that your plant has sustained.

If you are able to make a closer examination, you should be able to determine what those spots are. Here is a new article from Iowa State University that discusses both of these common pests and how to control them: https://www.extension.iastate.edu/news/2006/jun/070901.htm. What appears at first look to be powdery mildew, may in fact be spider mite eggs, or even scale insects.