Good afternoon, 

Thank you for contacting the Colorado State University Extension Lawn and Garden Help Desk with your question about your burning bush plant. 

It is likely that the browning of the leaves it is due to water and heat stress with the hot and dry weather we've been having lately, particularly combined with the added heat of a stone mulch. However, it is also possible that you could be experiencing an insect issue. 

There are three insects that can be problematic on burning bush plants: the twospotted spider mite, winged euonymus scale, and the euonymus caterpillar. This link gives methods for identifying which of these pests you may have as well as management techniques : 
https://www.extension.iastate.edu/news/2006/jun/070901.htm.

Please don't hesitate to contact us with any further questions. 

Happy Gardening!

Michelle D

Colorado Master Gardener Apprentice