Usually this happens from friction where the derailleur cable is routed around the bottom bracket. When the frame is flexing the cable moves with it. If you reduce the friction in the area, the cable will float and not move with the frame.

Usually a few squirts of chain lube onto the cable where it is routed around the bottom bracket fixes this problem. If that does not work try replacing the cable with a new high quality teflon coated one (don't use cheap ones).