If you're having trouble with your Xbox 360 controller staying on, try taking out the battery pack and bending the metal tab on the back out. Also pull the springs that touch the batteries up with a screwdriver (knife, scissors, whatever). Alternately those controllers have bad battery indicators. Sometimes all you need are new batteries, even if it says you don't.
I don't have a 360 myself, but I saved my friends $60 they'd have spent on new controllers with these methods. I'm a PS3 man myself.