Do you know the variety? Some are more prone to mildew. They do need plenty of sun and air circulation to help fight this disease. (a fungus, Erysiphe lagerstroemiae)
Best to chose a mildew-resistant type. Almost all of the newer ones are resistant, like the ones named after tribes of native Americans.
I read online some suggestions of what to use: To control, use a spray in early summer with neem oil, horticultural oil, Natria Disease Control, Daconil, or Immunox. The first three are natural products. You most likely will have to spray more than once.