Okay, I just replaced the firmware that was on both mini 0806's (0806 FW 20150511 v1.0) with Nigel's version (0806 FW 20150320 v1.0) I'm taking a 3-hour road trip today so let's see if that makes a difference.
For the first few hours of my 3-hour road trip on Saturday everything was fine. Then, about 2-hours in the mini 0806 began restarting. I think it restarted a total of 6 times. Then it turned itself off and simply displayed a blue charging light. About 1/2 hour later it restarted. The rest of the day it was fine. This was with the cable plugged directly into the mini 0806.
Sunday morning, it worked fine for an hour or so. Then, it started making a loud squealing noise. Rather than unplug it, I just let it go to see what would happen. About 5 minutes later, it shut itself off, but the blue light was still glowing. After another 5-10 minutes, it powered back on and began recording. It seemed fine the rest of the day. Sunday night, we started the 3-hour drive back home. Not one single problem. I haven't checked it today.
To me, this still sounds like an intermittent disruption of power that's triggering a low-battery situation. The USB adapter seems fine, and so do the Monoprice cables. However, I have noticed that every time I have an issue with this mini 0806, the voltage under load drops from 4.8v to 3.5v and the amps drop from about .45 to .14. Does this behavior sound familiar to anyone?
The last thing I'm going to try is swapping out the 12V cigarette lighter socket. My theory, which Joel pointed out above, is that the USB adapter is making intermittent contact with the 12V cigarette lighter socket or simply has a short in it somewhere. I believe that is causing inconsistent power to the mini 0806, which in turn is forcing the mini 0806 to use it's internal battery. At some point, this places the mini 0806 into a low power situation, which triggers a variety of weird anomalies.
Any other suggestions are very much appreciated.