Why does my Xbox 360 controller keep shutting off on its own?
Solution 1:
I've experienced this personally before. Basically, the connection of the battery pack to the controller no longer works properly, and can disconnect, even randomly, based on the level of degradation of the connection.
From memory, buying a new battery pack/switching it with another controllers pack can fix this, but the most reliable fix, other than burying a whole new controller, is getting a charge cable. This will ensure your controller has power when in use.