I suggest you clean your tension disks. You can use dental floss, or you can take the tension apart and clean each piece individually (if you do this be sure you pay attention to how it goes back together). When we first bought our GrandQuilter we had the same type of trouble, and the dealer told me to do this. If you have the tiniest piece of lint or thread in the tension it will cause you to break threads.
Also make sure you have the quilt at the right height relative to the machine bed. You should be able to slide your fingers between the take-up rail and the machine bed.
Hope this helps.
Darren