If the chain only falls off when going uphill, it might be something to do with your shifting technique. Maybe try easing off the power as you shift, or better yet, get in the habit of shifting to the smaller chainring before you get started up the hill.
my wife had this problem on her triple. We went so far as to replace the front derailleur with a better one, but she just couldn't get the hang of it. I "fixed" the problem by removing the big chainring and putting a chainguard on, forcing her to ride in the middle chainring all the time.