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From a GameFAQ's article:
When it rains or snows, there is a chance that some pieces of the fence will
break. You should always thoroughly inspect the day after a storm. Broken
pieces can be removed with the hammer and then replaced. If you have any
broken pieces, there is a chance wild dogs will come at night. The dogs are
characterized by high pitched barking after you go to bed, and they will eat
any chickens you leave outside (you will find chicken feathers the next day).
The more broken pieces, the greater the chances that dogs will come. Once you
exceed about 15 or so broken pieces, the dogs will come every night until the
fence is fixed.
I can verify that I have experienced this in-game.