I've been using 10.10 on my notebook for about a week, as it started to behave like this: Sometimes, while booting (while the "Ubuntu"-picture is showing, the one with the 4 dots representing the progress bar ), it shows " ######.#### restarting system", where #'s are "random" numbers followed by a reboot. I thought it could have something to do with usb-devices (I thought I've read something like that somewhere), so I tried unplugging - which didn't improve anything. Does anyone have a clue in which direction I should dig? Google is no big help for me here, because I'm kinda lacking good keywords.
IIRC, typing escape during boot will give you something a lot more verbose. Try to catch what happens before the reboot. Alternatively, the system logs in /var/log/syslog, if you look for the time before the last reboot, should have some info.
Edit, wild guess: maybe you are dual-booting, the other OS tells the bios it is doing a reboot, no one clears that, ubuntu see the "reboot" flag, interprets it differently and reboots.