If you have the Johnson pump with the electronic level switch I suspect your problem is with the electronic sensor. It has two small openings to detect water level and it can clog easily. To verify that this is the problem, check the wiring at the bilge pump and remove the inline fuse in the electronic control circuit. The pump should start and stop with the manual control switch. The sensor can be cleaned with wire dry spray using the small tube to squirt it around in the sensor. The problem is that it does not seem to last long. I have cleaned mine twice only to have it act up again within a few weeks. I am going to replace mine with a simple float type. As of now I am manually checking it every day and the secondary bilge pump is my back up. It had the same problem too but after cleaning it it seems ok for the moment. My personal, unsolicited opinion is that the electronic sensor is #@^&%$#!
If you don't have the same switch as Ladybug, Too, my apologies for my rant.
Pat, Ladybug, Too