Sheldon: That sounds a lot like it's frame flex causing the issue. Either the alignment of the BB/chainrings and derailleur is changing, or the flex is causing the length of the cable run to the derailleur to change and having it help shift the chain to a different ring.

Another possibility is that you've got some bad chainline issues, which are exacerbated by frame flex.

Is it climbing to a bigger ring, or shifting down to the small ring from the middle ring when you're accelerating? Are you in your biggest cog at the back when you're starting?