I had a similar problem with my bike. The LBS didn't measure my chain but they replaced it and the problem was solved. Seems like a pretty simple (and cheap) thing to do to start eliminating possibilities for the root of the problem. I didn't even know you were supposed to be cleaning the chain. Now I use a degreaser every other week or so (it doesn't rain much now since the drought but there's plenty of dust kicked up!) and I've had a lot more luck getting the chain to last longer and I don't have the dropping problem anymore when I apply more power.