We have never had that problem - our was the opposite. We would get enough vegetation sucked into the sump well and have it clog and stop. Luckily we were home whenever it happened so there was no flooding. That symptom though was our sump pump turning on, but because it was clogged with leaves and such couldn't suck so it would not turn off.

Our neighbor had his that followed the same kind of cycle that you are referring to. Where does your pump eject out to? If it ejects too close to the house, the water could be making it's way back into the drain system / pump well. The builder put his sump pump ejection too close to the stairs that led to his basement. when his sump would pump out enough water, it would make its way to his drain system and recirculate the whole process.