Are you straight stitching with a walking foot or free motion quilting with a darning or FMQ foot? Are you using polyester or 80/20 cotton batt? I have never had much luck FMQing on polyester. It just moves too much. I have better luck with the 80/20 cotton batt.
Is the quilt fully supported up on your quilting table so there is no drag? Are you quilting from the center out so any extra fabric moves to the edges? You might visit some sites to watch quilting done on domestic machines to pick up some pointers. Try watching Leah Day on the the Free Motion Quilting Project.