There can be many reasons why your Xbox 360 Kinect would stop working. Either a software or hardware problem, usually the Kinect for Windows SDK will have useful errors to guide you.
E_NUI_NOTPOWERED
This error happens either because of a driver install bug, or because of a broken or faulty adapter.
E_NUI_NOTREADY
This is a more generalized error, it has many causes. More often than not, reinstalling drivers will fix it.
E_NUI_NOTGENUINE
No, your Kinect isn’t a fake. This happens because of a drop in the USB data transfer speed, either because of a flaky cable, or because of a bad or overloaded USB controller chipset.
E_NUI_INSUFFICIENTBANDWIDTH
This error is caused by multiple scenarios, and as such the name may be misleading.