Maybe try searching the forums for cross-chaining. Maybe you're using a combination of gears that can sometimes lead to dropping the chain? (EX: Using big ring in front and smallest in back? Or vice versa?) I have to consciously make sure I don't get all the way to the top or bottom on the back before I shift up or down in the front. So far it's worked fine - no chain issues!
2007 Trek 5000
2009 Jamis Coda
1972 Schwinn Suburban
"I rejoice every time I see a woman ride by on a bike. It gives her a feeling of self-reliance and independence the moment she takes her seat; and away she goes, the picture of untrammelled womanhood."
Susan B. Anthony, 1896