Not 100% sure, but im pretty sure i have read somewhere that running RB on batteries, doing so using POE is not such a good idea. May be you could try using the power jack on the board rather than the POE?
I have Routerboards running on batteries using PoE no problems, installations dating back to 2004. So its not POE/Power injector that myth is debunked. Using a passive PoE w/ a DC input voltage is no different than running it on DC power from the power jack or running it off a standard AC -> DC PoE injector.
To troubleshoot this problem effectively you should probably eliminate the power concerns by plugging these devices into a reliable power source and rebooting to see if you can reproduce the symptoms. Or using a multimeter to ensure the batteries are producing a constant operating voltage with the load connected.
You could try downgrading to the 4.11 release as omidkosari suggested. I've yet to confirm the bug he's reporting and have not heard any confirmation from Mikrotik, but it appears others have had success with this release.
I'd be interested to hear what your findings are once you fix this problem.