Peonies are generally resilient, but they can be susceptible to issues like powdery mildew, botrytis blight, and nematodes. To prevent these problems, ensure good air circulation around the plants, avoid overhead watering, and remove and dispose of any infected plant material promptly. Regularly inspect your peonies for signs of pests like aphids or spider mites and treat them with appropriate insecticidal soap or neem oil if necessary.