Hmmm, I was trying to ascertain if your cover is held on by some sort of sheet metal screw (pointed end) or a machine screw (like a bolt, with a flat end). And if it's stripped out or not. It sounds like you've got a stripped machine screw. Perhaps it was cross threaded at some point.
Can you retrieve the screw? Are its threads OK, or crossed up?
Either way, if you can't easily tighten the screw, it's going to be a bit of a challenge under water: you can't use a drill or driver, and you can't apply enough weight and/or torque to force it in.
Some words of caution:
- If you attempt to work on this yourself, while holding your breath, please be sure to have someone standing by. An able-bodied adult who could perform a rescue if necessary. Just a precaution. Shallow-water black out is a real thing and you won't even know when it happens. You'll just go to sleep, forever.
- I'm not sure if fields_g was joking or not about the Spare Air rig (I have one of those). That might be tempting, just know that as soon as you take a breath at depth on an air tank, you're SCUBA diving and should know more than a little about it. You wouldn't get into much trouble if you were quick about it, especially if your pool wasn't very deep, but if you spend time at depth, you should know what you're doing, SCUBA-wise.
- Kudos for pursuing this repair. A loose drain cover is a potentially dangerous thing, and they have claimed lives. There really shouldn't be anybody in a pool with a loose drain cover. And if you or anyone else works on it, be sure to turn off all the breakers to the pool pad, so there is no possibility the pump can engage while someone is near the drain.
OK, all that said, without draining the pool, if you can't swim down and tighten the screw yourself, I think your best bet would be to hire a diver and have him go down and see what's up. You could call local pool maintenance companies for references to divers. Or are you near a coast? Try a local SCUBA shop. You might find someone to jump in for 50 bucks. He can try to tighten the existing screw, but the challenge will be holding himself in place while attempting it (not unlike space walkers trying to work in zero-g). If that doesn't work, you could use a stainless steel sheet metal screw that will bite into the existing threads enough to hold the cover properly. Not ideal.
If it's stripped or crossed, the correct fix is to re-tap the threads and replace the machine screw. You can try the same size, or you might have to go up a size. You'd have to have the right size tap (which you could figure out with the machine screw at a hardware store).
There's other tricks if those don't work...
