My first thought too. We recently had a grounding issue with our electric service that caused even our clothes dryer to not want to start every time. Consumers ran us a new ground and our flickering juice cleared up.
If your pump has a piggy back plug, as someone else suggested, than just get a new switch if it isn't a juice issue. Float switches are most dependable, but you have to be careful to give them room for their motion. Pressure switches suck. I love Zoeller pumps but I've had issues in the past with their switches. I prefer a pump with a piggyback plug.