Haven't got much time to answer you but it could be because of compiz or some screensaver, disable them. Some older posts describe a similar problem ...
ah haaaaaaaaaaa no compiz but I do have an active screensaver thats supposed to come in at just around that time! many thanks!
If this is really the problem, you can use something like this to start the game from a terminal:
alias oa="xset s off && /path/to/openarena.x86_64 && xset s on"