What conditions make the leaves turn red?
If your shrub has been heat or drought stressed this year, it may slide early into fall colors and dormancy as a protective measure. Make sure it is watered all the way into winter. A stressed plant is more susceptible to winter dieback. If there is any reason to suspect nutrient deficiency causing stress, have the soil tested. Euonymus diseases typically turn leaves brown. If red leaves are only happening on a few branches, cut off a section and examine the pith or inner core. It should be white. Verticillium wilt develops brown or purple streaks in the pith. Affected branches should be removed as well as fallen leaves and any mulch. Keep cutting back until white pith is found.
Your burning bush should naturally turn red in the autumn. In order for this to happen, though, it needs at least 6 hours of full sun. So if it's not changing and you think it should, it might be time to move it to a sunnier spot. This article will tell you more about burning bush care: