The problem is still occurring. Woke up this morning and the notification light was blinking, but the power switch wouldn't turn it on. One thing I noticed though is that when I rebooted, after the Google logo appeared, I looked away for a few seconds and when I looked back it was at the lock screen. It couldn't have gone through the whole boot process with the X. Looks like I'm going to have to take it back. Bother.
The battery was also drained, but it appears that the issue is a bug in Bejeweled which leaves the Media Server process running constantly unless you use Fast Reboot or a task manager to kill the process. So lame, EA.
One data point about the short reboot time: GSam battery monitor shows the up time as being a few seconds while the Android battery graph is reflective of the actual unplugged time.
Posted via Android Central App