Did the package include a lock-washer?

It's probably loosening up because it's hard to get at the nut and it hasn't been tightened enough to keep it from getting loose after the faucet is rotated. Some faucets have a lock washer or gasket, some come with a special, long tool that gets secured on the nut and allows you to tighten it from beneath the sink, and some you need to use a basin wrench on:

Basin wrench

You could talk with tech support for the manufacturer and get their advice, or at least find the installation manual online to look at how it's supposed to go in. There is usually nothing magic other than using all the parts that came with the faucet, and getting the mounting hardware tight enough that torquing the faucet repeatedly won't cause it to loosen.

I do have a basin wrench, and that's what I use to tighten it-- impossible to reach otherwise. I'm reasonably strong and have broken my fair share of bolts; I really don't think I'm under-tightening.

There is an 0-ring to seal the faucet against the granite. I used it as it came, with neither added lubrication nor did I clean off anything that might have been on it -- so it had a light oily film typical of new o-rings. I suppose I could try to get rid of anything slippery in hopes it would catch better.

Nothing that looked like or would function as a lock washer. The hole in the granite is, of course, round, so nothing there for a lock to catch against.

Calling the maker is, of course, a good idea. I was just afraid I was missing an obvious step that everyone else knows about that the manufacturer might be reluctant to recommend, like roughening the granite underneath.

It wouldn't be so bad except that it's really awkward to reach and my aging body doesn't like to bend that way anymore. I guess I need to pay for my "free" faucet somehow!

Well, it sounds like you know what you are doing. I once had something like that happen because there was a slight obstruction by the sink that kept the nut from seating properly. However, if there are no issues like that and you have all the mounting hardware in place, I'm out of suggestions. Adding lubrication is probably not helpful, or could possibly make it worse. Hope you get some insight from the manufacturer. Looks like a very nice faucet otherwise...

Clear sealant around the base of the faucet may be enough friction to keep it from turning.

Vith has a good idea with the clear silicone. First you need to make sure there is no 'grease' on the bottom of the faucet or the counter. Rub with alcohol and paper towel.

You could try a second nut to hold the first.

Thanks, I like both of those ideas. I've been using an industrial urethane sealant on my trailer that grabs much more tenaciously than silicone. I can give that a shot and add a second nut or a little thread lock on the nut while I've got it apart. Good ideas-- but I better make sure its right before the stuff sets up!

Good luck...but also don't glop on too much adhesive that the faucet can't be readily removed when/if it needs replacement or maintenance.