With ''turn off'' what exactly do you mean ?
Does the card stop working (meaning the fan(s) on it stop working too) and then starts working again or you have no image on the screen and then suddenly after a while you have it again ?
I've had problems with my 8800GTS with driver crashing, but that's Nvidia, not ATI (AMD). So you can change/update your drivers to your card and see if it still turns off like it did.
By the way, can you post your whole configuration, because your PSU might be too weak for keeping everything up running (Shouldn't be a problem as it's a AMD card and they don't need much power to run). But you never know...