I have some sort of animal or insect destroying my thyme plant. Each day I check on it, to find something has seemingly clipped the stems of the plant and left the clippings in the dirt beside it. The leaves do not appear to have been eaten at all, just the stem snipped off. Anyone have any idea what could be doing this and any ideas on how to keep that predator away?

It is in a pot on a balcony in Brooklyn along with Mint, Rosemary and Parsley. All other herbs are unaffected.

I am new to this, so any help is appreciated. Thank you in advance!