Peonies suffer from very few pest and disease problems. Nevertheless, they sometimes get fungal diseases, such as botrytis blight, which you describe. Other similar problems include blackened and/or rotten stems, withered buds, gray mold near the base of the plant. In all cases, remove and destroy the infected plant parts. Make sure the plants aren't getting overwatered; avoid sites with poorly drained soil. Good air circulation around the plant will also minimize fungal problems. Powdery mildew can be a problem near the foundation of a house, where there is lots of roof runoff and splashing. Consider moving the plant to another location if you see powdery mildew every year. To prevent problems, do a thorough clean-up after fall frosts. Cut the stems to 3" from the ground and clear away the foliage.