Android device crash logs?
If nothing can be retrieved from logcat you are probably running into a kernel panic.

You could check via adb the output of: dmesg

Some devices also have a kernel feature where, on critical errors, the last received kernel message can be read from /proc/last_kmsg 

Maybe this will give you some hints whats going wrong. 
If not you could stream the full kernel logs via: cat /proc/kmsg and reproduce the shutdown while doing this.