I had the same Nashbar grocery panniers and we had the same problem. Reusable grocery bags did not solve the problem unless you only filled them about half full and then tied them at the top.

I switched to the wire baskets and never tried a pair with a wire frame. The Nashbar panniers feel fairly stiff but they don't hold up under a load. My husband occasionally uses them for the farmer's market but we've had a lot of veggies fall by the wayside.