Usually the leaves of my peonies stay green and pretty until the first frost, but this year (it is September) something is eating the base of the stems, making the stems and leaves die and fall over. What varmint would be responsible for this?
It may be that you have picked up a disease called “crown rot”. You can read more about it, and other peony diseases, here: http://www.missouribotanicalgarden.org/gardens-gardening/your-garden/help-for-the-home-gardener/advice-tips-resources/visual-guides/peony-problems.aspx
If they are actually bitten off then I’d suspect chipmunks or red squirrels. We have a spray called Repels-All that will keep them and other animals away.