Radeon Xtasy Video Cards tend to run hot. More so when under load.

From what you have described its a heat problem.

To test this pop the side off the computer and put a desk fan blowing into your machine.

Run for a few hours to see if the error happens. If not its heat. You'll then need to look at a 3rd party cooling solution for the card or extend the cooling for the case in general.

If you still have errors, its then likely to flaky video card drivers. Download latest version and try again.