Jeff, as is often the case, the answer is "it depends." On our farm we are constantly monitoring water temperature and dissolved oxygen through the summer months. We get a feel for the daily fluctuation of oxygen levels, and usually set timers to turn the surface aerators off for 4 to 12 hours a day, depending on density of the fish, water temperature, amount of vegetation in the pond, water flow, et cetera. You do need to be careful during extended cloudy periods, as you can have a cumulative drop in oxygen.
Generally, in low density recreational ponds you can shut down the aerator for the day light hours, but it is hard to give a totally up or down answer.
One added benefit that we have found from shutting down the units during the day (besides electrical savings) is that they tend to not clog anywhere near as fast. Yours may not clog at all in a recreational pond, but in high organic load ponds, and ponds with a lot of algae, they can really clog quick. Kascos are good units.
Mike Robinson
Keystone Hatcheries