I have this problem too, except my mouse usually has trouble scrolling back up. Pressing down hard on the little scroll ball and swirling it around usually fixes the problem. Apparently, using canned air occasionally can help quite a bit too.
Well, it turns out, when the Mighty Mouse scroll wheel gets dirty, it stops being able to scroll down. Apparently, it’s a common problem, as a quick Google search turned up tons of pages, like this one at MacOSXHints.com.
The fix? Blow compressed air around the scroll ball, or just push on it really hard and roll it around (that worked for me). If you’re lucky (I was), it will start working again. If it keeps doing it, though, I’m going to have Apple replace it.