But, if the game server was correctly shutdown, the server could know it.
Let's says it's 00:00. Time for server to reboot. The script would shutdown the game server properly, and then creat an empty file named "correctShutDown", then launch the server "reboot" command.
Then the server reboot, and launch a script at startup which would check for this file.
If it exists (means, the server didn't crash, it was a clean reboot) then remove the file "correctShutDown" and start game server automatically, else, send a mail, sms, whatever to devs.