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Can you include a photo and your USDA climate zone? This will help me to identify your issue.

Of coarse you should abide by your regions list of invasive plants. Many gardeners have great success with Burning Bush plants with no issues of them self seeding and invading.
I am one of those gardeners, I have never even had a seeding pop up around my two Burning Bushes.

Several diseases can affect burning bush plants, including cankers, fungal spots and powdery mildew. One of the most serious is coral spot nectria canker, a fungal disease that can causes discoloration and growths on bark, cambium and sapwood and can cause dieback and eventual death of the plant. Since weather stresses are often a cause, avoid pruning burning bush shrubs in drought or summer months. Serious pest infestations include winged euonymus scales and the spider mite. A horticultural oil, insecticidal soap or insecticide may be required during severe outbreaks.
https://www.gardeningknowhow.com/ornamental/shrubs/burning-bush/burning-bush-care.htm

Each spring, feed the burning bush just after the plant begins to put on new growth. Use about 1/2 cup of tree and shrub fertilizer per bush. Sprinkle the fertilizer on the ground over the root area of the bush. Rake the granules into the top 1-inch of soil and water thoroughly to start the fertilizer traveling down to the roots.
https://www.gardeningknowhow.com/ornamental/shrubs/burning-bush/burning-bush-care.htm

Depending on the variety they can reach from 5 to 15 feet tall. You can train it into a small tree, rather than a bush, but it will require constant maintenance to remove lower growth. It will never stop trying to recover that growth at the base.

This article will give you more information on the care of these: https://www.gardeningknowhow.com/ornamental/shrubs/burning-bush/burning-bush-care.htm

They will normally turn red. This will be expected. If you are experiencing leaf drop, then I would mark it up to a fungal infection in the soil. There are several ways to control this, but using wettable sulfur and dolomitic lime will be the safest, and most effective way to control this without harm to the soil or plants.

This will prevent, and spot cure any infections, especially if you live in an area that remains wet for long periods of time.

This article will give you more information on the care of these: https://www.gardeningknowhow.com/ornamental/shrubs/burning-bush/burning-bush-care.htm