The problem your having is that the little rubber end piece that fits into the impeller cover has dried and shrunk over time. It used to hold the impeller in place. I fix that by stretching a piece of the rubber band over the end then, placing back into the impeller cover. You might have to use a little force to get it in. Be careful you don't want to break the shaft. cut off the excess. put the impeller cover back on. make sure the it doesn't get pulled apart when you put it back in. this should suspend the impeller making it start everytime. I hope this fixes your problem.
Yuki