Certified GKH Gardening Expert
This is, actually, quite normal for most of these shrubs. You can't stop this from happening, but you can cut off these dead blooms. This can help encourage a second flush of flowering in many cases.
This article will give you more information on the care of these shrubs: https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/crepe-myrtle-care.htm