I got to say that I have had my Xbox for about a month now and I used it for countless hours at a time sometimes up to 60 hours without turning it off and never had a problem. Then about 5 days ago my xbox started turning off and well my first reaction wasnt to bad as i thought maybe the cord got loose or something. I checked everything and made sure everything was fine and noticed the red light had turned on the power supply. I disconnected the power cable and reinserted but about 30 minutes later turned off again. So this time I put a fan thinking it was overheating which I knew it was kind of odd because my xbox was working during the whole day and it was about 98 degrees in the room. well i already had the power supply suspended as the cable was too short let the power brick touch the floor. well tried everything but kept doing the same thing. So finally I tried the last thing that could possible change everything I disconnected the power supply from my surge protector(monsterpower Hk-1000) and plugged it in the wall socket and so far so good. It hasn't happened and it was very hot today again it reached about a little over 100 degrees.

I don't think it overheats I just think that a surge protector gives it a constant power flow and seeing as how an xbox consumes a nice chunk of it and not only that but consumes it in a fashion which is unpredictable that it ends up being incompatible with most surge units. I don't know if I made sense but I would suggest connecting your unit to the wall before you try anything else. The xbox 360 manual also informs of the power supply being connected to a wall socket rather than anything else. 

                Thanx guys for all the info you guys provided never would have figured that 1 out!