Answer: It sounds like powdery mildew, which many zinnias are susceptible to. Powdery mildew appears as a whitish/greyish powder on foliage. It overwinters on living plants, and can be difficult to eradicate. If the zinnia plants are declining rapidly, you may want to simply remove them. It's unlikely you'll be able to control the disease in time for these heat-loving plants to recover and put out more flowers before cool weather sets in.
There are some things you can do to minimize its effects next season. The first line of defense is to grow resistant varieties. Also, be sure to space plants properly for good air circulation, and thoroughly clean up plant debris at the end of the season.
Powdery mildew is unique among common plant diseases in that it doesn't require a wet leaf surface to spread. It can thus thrive during hot, dry weather. The general advice to inhibit the spread of fungal diseases is to avoid wetting leaf surfaces. In the case of powdery mildew, you can actually inhibit infection with frequent sprays of water. Also, examine plants frequently, removing any affected foliage immediately.
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