are you using a free-motion (hopping/darning foot?)
you could be pulling on the fabric more than normal-
if you've been doing this for a while- and this is a new developement prehaps there is something (lint) build up in the bobbin area? or could just be not the right needle for the thread for the fabric combination- but it really sounds as if you are pulling too much on the fabric- machine is going slower than you are-try speeding up the speed of the machine- while slowing down your pulling/manuvering-and the correct foot in place correctly-
sometimes it takes a long time to get the hang of it on a new machine- make a couple small practice pieces- and work with those to get the *bugs* worked out before trying to do an actual quilt- you may need to gradually increase the size of your practice piece before you are successful on a large quilt....with a small practice piece you may be able to (pin-point) the problem- actually see what happens that causes the needle to break---is it hitting the foot? or the plate? or bending?...with a small piece you should be able to see better the cause- then will have a better idea how to fix it