Logcat should get you through.
So do the trace file and the tombstone file.
adb kill-server has nothing to do with it.
If you kill something from the shell, it depends on the signal type.
You will find all "watchdog" related events in the log, and if you customize your own ROM, and want to ease the finding of those events, you can add a single line to the zygotte block of your init.rc
-Ron Munitz
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adb shell cat /proc/last_kmsg should give you the messages that gets missed from adb .
You can monitor the serial console logs too.
From logcat you can look in Shutdown Thread for reboot reason, if its soft/hard reboot.
If reboot is due to crash you can rely on pstore/last_kmsg/serial logs.
Hope that helps.