Are you sure the float switch is working? If the sump fills slowly the switch may stick, then when you pull the pump and drop it back in it may jar the switch enough to make it work.

Thanks for taking the time to respond. A stuck switch was my first thought as I realize that switch problems are the #1 issue with sump pumps. BUT the sump pump is sitting in the water doing something -- it is a loud buzzing which suggests to me that the motor is actually running even though the thing isn't pumping; I presume (correctly or not) that if it was a locked motor it would buzz but not as loudly.

Because of a lack of alternative explanations, I'm starting to lean toward an intermittently bad motor. I think I'm going to have to bite the bullet and get a new sump pump!!

Your issue sounds mechanical rather than electrical. A locked up motor or one with an open starting winding would hum rather than buzz. If you lie the pump on it's side and jog the float switch can you see the impeller rotate smoothly? A buzzing sound might indicate a detached impeller or piece of debris caught in the casing and fanning the impeller vanes as they pass by. A bad bearing will usually make a dry grinding noise.