Hi Greg
I wonder if it is gofers? I was at a friend’s garden near San Diego and he had to put chick mesh wire under his growing area as well as on top, to grow pretty well anything!
The mesh we have here is tradename Enviromesh, lots of nylon filaments in close woven squares, reasonably light so it can often be laid on top of plants without support. In wet weather though it can become too heavy for small plants but that may not be an issue for you.