Hey James Madden,
It is not recommended to automatically reboot GeoEvent on a periodic basis. If you can avoid that, it would probably be a good thing. If you do have to reboot, as a safety precaution, you should turn off all of your GeoEvent inputs, services, and outputs prior to stopping the GeoEvent Windows service and rebooting. Once the machine returns to life, restart your GeoEvent outputs, services, and inputs (in that order). Doing this ensures that things start up in an orderly fashion and all dependencies are accounted for.
If you are in a situation where you are forced to automatically reboot the machines on a periodic basis. I would implement a python script to run on shutdown and startup that performs the stop/start operations for you. You can find instructions for how to do that in Andy Ommen's article Scripting Tasks Using the GeoEvent Admin API.
Best regards,
Eric