Answer: Based on your description I am not certain what is happening to your peonies. Since you have lots of foliage, I think there may be a problem with lack of maturity or excess shade or possibly low fertility. Maybe the following will help you trouble shoot.
Rather than being a bulb, peonies have tubers with "eyes" or growing points. Newly planted peonies often take two or three years to settle in and begin blooming. If the tubers were very small at planting, it might take longer. Peonies that are planted with their "eyes" deeper than one to two inches (or that settle deeper after planting) may not bloom well if at all. Peonies need full sun to bloom well, in shady areas they bloom less and sometimes not at all. Peony stems and foliage should be left intact and growing all season, they keep the plant healthy so it can renew its strength and bloom the next year. Remove these in the fall after frost has killed them. In the spring, top dress with good quality compost and a general purpose or slow release granular fertilizer such as 10-10-10 or similar proportions. Read and follow the label directions for how much to use. Finally, sometimes late spring frosts can damage the flower buds.
If you think there is a problem with the tuber, such as rotting, I would suggest you consult with your local County Extension to try to obtain a more specific diagnosis. Based on knowing that, you can decide how to proceed. If a chemical control is needed, they will have the most up to date information on what to use and how/when to apply it for best results.
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