The outside edges of my hot pepper plant are being eaten, and there are no visible signs of insects.
In our community gardens I have seen, but not in my plot, flea beetles which attack various crops, but this is something that is eating large areas at the edges of leaves and distressing some of the plants. Most are wild heirloom hot peppers (Thai, Bolivian, a variety from Bartram, etc.)
Answer
It sounds like you may have a "Cricket party" going on in the garden, with the grasshoppers invited. Crickets and grasshoppers chew on the outer leaves and trunks of the the pepper plants. The crickets work at night and the grasshoppers continue the celebration during the day, welcoming squirrels and others. Do not plant peppers where tomatoes, eggplant or potatoes, were previously grown. Keep your soil moist, and do not apply too much fertilzer. Last but not least, try an soapy water spray on your pepper plants. Use 1 tablespoon of Ivory Soap to one quart of water and spray away.