This is an issue I have noticed six months into ownership of my Librem 13. When moving the screen during use - it will occasionally reboot the laptop. Other times, the boot sequence will fail - or the screen will be filled with blocks of inverse and flashing text that will persist until I force a reboot.
I took off the rear panel, and disconnected the battery, and checked all connectors. Then I reconnected the battery. At first, the screen refused to come on, while the Librem booted as normal. After several attempts, the Librem 13 v3 now functions normally.
I believe there is an intermittent bare metal contact between the MB and the case. I intend to put a thin non-conductive sheet to cover the MB in some areas - so long as cooling is not affected.
I will update this topic with my progress. Any and all suggestions are cheerfully requested. The Librem 13 is an outstanding piece of hardware.