It's best to run the aeration at my pond 24/7, but some, maybe most, ponds can do with less. There's a lot of variables to know for sure without testing your particular pond's environment. I'd say, in general, running a properly sized system 24/7 is best, but may not be a necessity.
Luckily at my pond, when I get a lot of rain (spring and fall) that causes excessive throughput...the rain temp and pond water temp are very close to the same. But, if the temp difference is large enough along with any chemistry differences this can cause stress to the fish.
An undersized aerator can cause problems given that it is not moving enough water to eliminate all the dead water at the bottom. A fresh and large inflow of rain water of a different temp than the pond water can cause the pond to turn and the dead water mixes in too quickly. This would be hard on the fish.
