Answer: There are many possible reasons for the lack of flowers:
The plant is too young. Sometimes it can take 3 years to get blooms from a slow growing peony.
Not enough sun. With the exception of areas with very hot summers, herbaceous peonies generally prefer full sun. An hour or two less won't make much difference but heavy partial shade will reduce the likelihood of flowers.
Poor nutrition. Peonies are heavy feeders. If soil is poor or there is too much competition with nearby shrubs and trees, peonies will not flourish.
They are planted too deeply. Peonies should be planted with the top eyes on the crown no deeper than 2 inches).
Diseases can keep peonies from blooming. Peonies hate growing in wet areas! Rot sets into the crown and over time the plant weakens. I have seen peonies hang in for years in poorly drained sites but they don't flourish and eventually they succumb to the rot.
Or, Bud blast. This is when young buds are attacked by a fungal pathogen or late frost. They won't fully develop and you won't have flowers.
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