It sounds like the pump switch is either failed "on" or is hung up on something, keeping the pump running. When you unplug it, some water drains into the pit, and when you plug it back in, the pump then pumps out the accumulated water.
Either way, you'll have to remove the cover. Most of these "sealed" covers are bolted down to the sump pit. You will also probably have to disconnect the pipe(s) leading out of the pit to get the cover off, unless you can just slide it up on the pipe(s).