I'll have to find the post, but someone used a small BB (it actually looked good) in place of the scroll wheel and has had no problems. I'll search it out.
Cleaning...again and again...and again...and again...then bin it.
Clean the mouse and all should be fine. I had this same problem. By the way, it will become a shorter interval of time before it stops working after cleaning again. You will eventually learn that it sounds good, but it a load of crap as you hardly ever scroll sideways. Then you will get sick of cleaning it and get a better mouse. You will probably decide on a logitech or a razer (www.razerzone.com) mouse, as these seem to me as the best two mouse companies on the market.
In short-don't buy an apple mouse as they are made for aesthetics > ergonomics. (or to look good in common language)