I got my first VZ GNex on 12/16. It worked fine for about 7 - 10 days until the screen would turn of by itself sometimes while I was was using it and other times while it was laying on my desk (not timeout). Sometimes it wouldn't come out of sleep mode, or at least the screen would not illuminate when the power button was pressed. Sometimes when trying to get it out of sleep mode by pressing the power button, I could see the screen come on very dimly for about 1/4 second then go out again. When it did this, I could see the lock screen. But I was never able to get back to the home screen (or any other screen for that matter) without pulling the battery. This problem became more frequent with time. Initially, pulling the battery for 30 seconds did the trick. As time went on, I had to keep the battery out for about 10 minutes or so in order for the device to reboot!
So two days ago, I had enough of this and went down to the VZW store and they agreed to give me a new phone. So far, that problem has not recurred. However, today I was listening to Pandora and the SOB rebooted itself. To my knowledge, my first GNex never rebooted itself.
I did install LightFlow today, but have no idea if that may have anything to do with the reboot. If this continues, I will uninstall LightFlow and see what happens. But at this point and based on other posts here, I doubt it has anything to do with LightFlow.
Stock ROM, Unrooted.