Xbox 360 console turns off unexpectedly

Overview

 

The Xbox 360 console can unexpectedly turn off under the following circumstances:

-The Auto-Off setting is enabled, and the console has been inactive for six hours.
-The console is too hot.
-There's a problem with the power supply. 

Solution 1: Make sure the Auto-Off setting is disabled

-Start the Xbox 360 console without a disc in the disc tray.
-Go to the Settings hub and select System.   
-Select Console Settings.       


        








-Select Startup and Shutdown.

             









-Highlight Auto-Off. View your settings on the right side of the screen.










 
-If the Auto-Off setting is disabled, go to step 8.
-If the Auto-Off setting is enabled, select Auto-Off, and then select Disable.









 

-Turn off the console. Wait about 10 minutes, and then turn the console back on.
If the problem still occurs, note how long the console was on before it shut down, and then do one of the following:

If you have an original Xbox 360 console

    -If two lights are flashing around the power button, “Let the console cool down.”
    -If the console just turns off and there's no indicator light illuminated around the power button, “Check the power supply light.”

If you have Xbox 360 S console

    -If the power button is flashing red, go to the Flashing Lights Solution.
    -If the console just turns off and there's no indicator light illuminated around the power button, “Check the power supply light.

Source : https://support.xbox.com