You could make the maintenance once a month on days your monitoring shows already have about no traffic. If a HA setup, then fail-over, reboot main, fail-back-over, reboot other stuff. Minimal disruption there.
If you've got an HA setup you should probably be doing this monthly anyway just to verify that it actually works. The adage that an untested backup isn't a backup at all applies to backup internet connections as well.
