My Macbook Air 2010 (11 inch) goes black and needs to be restarted every 8 - 12 or so hours I have no idea why this is happening as nothing seems to trigger it. The computer just freezes and the screen goes off, and no amount of key pressing or brightness control jiggering will do anything. Only a restart will let me use the laptop again.

I'm usually not even touching the computer when this happens. One moment the screen or screensaver is on, and the next moment the black non-responsive screen of death happens.
This sounds like a problem with your logic board.

You can run a preliminary hardware test by plugging in your Mac OS X flash drive, and holding down the 'D' key when starting up. See this Apple support article for more info.

A bad logic board usually needs replacing, which can be expensive. Luckily, your computer is new enough that it should still be covered by your warranty.

I recommend that you take a trip to the Apple store so that they can fix/replace the computer for you.