Are you perhaps shifting too "quickly"? I guess what I'm really asking is that when you shift, do you push quickly, or hold the shifter a couple of seconds before letting go??

I did not have a problem with chain coming off, but I did have a problem of not being able to shift to the big ring and it was because I wasn't holding the shifter, just pushing it and letting go. I have Shimano gears.

I hope I am explaining this in a manner that makes sense. Hope its info you can use.