Two thoughts come to my mind because i have experienced the same problem in my yard.
Last year i had a bad grub infestation. When this becomes a problem, they tend to be close to the surface of your grass (eating the roots of your grass). Many different animals will forage for them. I've had crows, raccons, and possibly skunks making holes all over my yard.
My second thought is SQUIRRELS!!!! I've finally got those suckers under control. I call them "
tree rats" They are constantly digging holes in my yard (either burying or digging up accorns). If u have no squirrels or oak
trees, than i would look at the grub problem. I if u have a bountiful supply of night crawlers, the moles will go crazy for them. Are the holes really deep and continuous?
One thing i'm almost quite sure of, there is some sort of food in your grass, whether it be grubs, accorns, or nightcrawlers!