99.9% of residential aerators tanks around here work off of a float valve. sounds like there may be a problem with either the float, the rod thats attached to float, or the valve itself that the rod comes off of. take the top off the aerator and have a peek. .. if it only does it sometimes, sounds like maybe the valve itself needs replacing (sometimes when older they will hang and not go all the way up), but you should get a good idea when you take a look at it. aerators arent rocket science, when you push the float down water should come out.. when you pull the float up water should stop.
i'm gonna look like a pinhead when its a float switch.. but i'd guess float valve. many people here have pump&tank on well for aerator and outside water, then another pump&tank off aerator for home use.