Peonies should be cut back as the plants begin their die-back in late summer to fall. Cut the stems close to the ground and dispose of them to minimize overwintering diseases. Peonies are such beautiful plants when they are in bloom, but are susceptible to wind and rains. Then the large flowers get waterlogged or top-heavy and, as you say, flop over. Perennial rings or support can help to hold the stems upright. There is only so much that cages and/or supports can do.

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