Good news everyone! Microsoft has apparently identified the issue with Windows Phone 8 that is causing some devices to randomly reboot, and will be delivering an update over-the-air to devices sometime in December. They didn't specifically mention what the cause of the issue was, or whether it affects all new Windows Phones, but the good news is that there is a fix.
We’re continuing to investigate some reports of phones rebooting and have identified a cause with our partners. We are working to get an over-the-air update out in December.
The HTC Windows Phone 8X we have in our office here hasn't experienced any random reboots as far as we're aware, but for those of you who are annoyed by the issue you shouldn't have to wait much longer for a fix.