I don't know if you are doing regular, machine quilting, or free-motion quilting. I'll address the regular, machine quilting.
Try using a walking foot on your machine. This will help to keep both, the top and bottom layers moving in sync through the machine.
Also, check your throat plate. If it has a big, oval, needle hole it may be inviting fabric to get pushed down into the machine. If you have a different throat plate, with a small, round, needle hole, try changing to it and see how it works for you.
Make sure that the weight your quilt is not pulling on the machine. Give it some support by keeping most of the quilt in a corner of your table, or rolling it up on each side of the machine, so it is easier to handle.
~ C