What kind of spool of thread are you using? It sounds like something is catching the thread along the thread path. It might be the little slit in the top of the spool if that is the kind you are using. It also might be how the thread is feeding off the spool. Crosswise wound thread likes to come off the spool differently from stacked thread.
Since it is only breaking between the patches, is there a rough spot on the needle plate? Try changing the pressure of the feed dogs? Perhaps they are "chewing" too hard between the fabric pieces? Have you got the top tension on your machine set at the little red factory line? The bobbin tension should be firm enough so that you can dangle the bobbin by the thread and you have to jerk it slightly for the bobbin to descend? That's all I can think of off hand. Hope you can find what it is, good luck.