Answer: Based on your description, I am not certain what is damaging the petunias. Animals such as deer and woodchucks will eat the flowers. They can sometimes be deterred by using a granular or spray on repellent labeled for the specific animal, small animals can sometimes be repelled using pepper wax spray applied to the plant.
Since you haven't seen any culprit, it might be slugs. These are nocturnal and leave a silvery trail behind. You can handpick these at night and drop them into soapy water, or you could use a slug bait based on iron phosphate such as Sluggo.
Some insects might damage the petals. Budworms for example dig into the bud and then when the flower opens it looks partially eaten. Check carefully for tiny caterpillars or worms on the foliage near the blooms. If you think it is an insect you might want to consult with your local county extension to identify the pest more specifically. Based on knowing that, they can suggest what to use.
I hope this helps you trouble shoot.
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