If you just need to keep the nut from coming loose, try LocTite Blue (assuming metal thread and nut). You should be able to buy it at the local hardware store.

I had the same problem with a slightly different Price Pfister model sink. My problem was primarily because the sink basin was thin and not "beefy" enough to support the faucet. The whole thing would flex because the metal was thin and the nut would come loose.

Using wood for reinforcement down there is a bad idea (it would get wet and rot). So, plastic was the way to go.

I bought an inexpensive piece of plexiglass/lexan at the local home improvement store. A cheap plastic cutting board would work well too.

I cut a rectangle that was a couple inches wider than the the faucet holes and that would fit underneath the sink basin where the holes for the faucet were.

I marked the holes and cut them with a hole saw (Go slow, the heat from the hole saw will melt the plexi!). Cutting slightly oversize makes everything fit easier.

I put my new "reinforcing washer" in place and tightened everything down. The nut snugs up nicely against the plastic and after four months: no more flex, no more nut loosening.