Hello nma,
The HP ALM server should not require a reboot, other than what the operating system requires for normal usage and maintenance/update installation, if configured correctly. If installed and configured correctly the system runs background processes to systematically maintain the correct operation by running maintenance routines for cleanup and repair as needed within the background (and generally does so at times of lower system usage to avoid impact to the users.
If you are going to reboot the server the things to note are that all users are out of the system and they have saved their work upon exit. Also the DB must be up and running prior to starting the HP ALM services, as if the DB is not up and properly running, the HP ALM services will not start.
One exception that should be noted is that it would be beneficial and highly recommended to restart the server after altering the installation (rolling back to a prior patch level or installing a newer patch level, as this insures the system has cleaned up all residual files that may have been cached upon changes being made. It is always recommended to perform a complete and entire backup prior to any maintenance procedure being attempted,
Hope this helps,
Dan