I have 360 slim and I believe power adapter is bad. my xbox powers off and power supply has a red light on it. if i unplug and reconnect it's fine for about 10 minutes.
I would recommend you phone MS support for your region, and speak to them about getting a replacement adapter.
It is covered under the 1 year warranty.
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I did. It will take 5-10 days for replacement to arrive once they receive defective one. Thanks for reply.
No worries and good to hear your new one will arrive soon. Good gaming to ya.. :)