Chosen Solution
Hello, my Xbox 360 Slim just turned off randomly. It didn’t respond to the power button getting pressed. So I unplugged the power supply from the Xbox, after it booted up just fine but after 30 seconds it did the same thing again. (I heard a beep before it turned off.)
Sounds like it may be overheating. Have you cleaned the interior any? There may be a build up of dust causing it to overheat and shut off because it can’t cool the Xbox properly. Try opening it and seeing how much dust is in it, and if there is a lot take a brush and clean it out, and see if the issue persists. Hope this helps!