How can I determine the cause of random device reboots?
I had a similar random-rebooting problem, and after one such reboot, I hooked up the phone to my laptop and ran "adb bugreport" on it.  I got what looked like useful information, and attached it to the bug.  So I think at least some log information survives a reboot.

Here's the bug, btw: http://code.google.com/p/android/issues/detail?id=24118