Answer: I have seen both chipmunks and birds pick at and even remove flowers, maybe one of these is the culprit in this case. You might try watching in the early morning and see if you can catch the critter. In the meantime you might try using a rodent repellent, and possibly a scare crow or other bird scarer device. If on closer inspection you should find beetles, you could try a neem based spray as a repellent for those.
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