You could try to see if there is anything useful in /var/log/syslog
, however if the shutdown was sudden, you may have nothing there.
One thing you could do is to connect to the board over serial and see if you can catch some last-minute kernel log. Here I explain how to do it from another Bela, but any 3.3V serial adapter should do.
I have seen something similar happen in response to a brownout event: the 5V power line having a sudden dip would cause the SD card to be re-mounted read-only and everything stopped. If you have external electronics connected to the same power supply (e.g.: a solenoid or other device that absorbs spikes of current) that could be a reason.