I agree with Mr H... can't live with it anymore - though I used to wonder why I ever needed it
I find it great for composing landscapes with the sun in frame (so I don't have to burn my eyeballs looking through the viewfinder), all macro work - the viewfinder is usually in a difficult-to-reach position, precise focusing on a tripod, and getting feedback in real time. The 5DmkII (and presumably 600D) also has a silent shooting mode in LiveView.
If you're tethered to a laptop, seeing the LiveView display on the laptop screen is fantastic. (When in this mode, you can press the LiveView button on the camera again to see it on the back of the camera too.)
Btw, the switching off is just the camera's normal sleep timer - disable or extend it in the menus.