[OrlyP]

As what was already mentioned, you only need to stop it to do maintenance and refueling. But on the flip side, there's also no reason to keep it running if you have little need for it. Doing so helps towards conserving your fuel or even your stash of motor oil. This is especially important if the duration of the outage goes beyond your stored fuel or the next oil change interval if the generator were to be used extensively or continuously.

Plan and prep ahead. Aside from fuel, keep consumables on-hand like extra bottles of motor oil, spark plugs, etc.