I know this is an old post but I have had the PQ1500 for years and have had the same thread breakage problem, Especially when doing free motion backward. If your breakage is on the straight forward stitch change the needle and re-thread the machine. Good news is I think I've solved it. I think Brother has designed the thread passing through the needle wrong.
The needle is placed in the machine so you have to thread it from the left to the right. (I did go check the instruction book) But look at the thread carriers, they don't carry the thread down the length of the needle through the scarf of the needle, the thread goes from the thread carrier to the needle sideways, so of course there is fraying. The little groove in the needle above the eye is there to direct the thread through the eye of the needle and prevent fraying.
To solve this I used a small piece of paper clip, bent it to form an additional thread carrier, placed it above the last thread carrier. This directs the thread straight down through the scarf of the needle. Since I did this I havent't had the thread break once. Can't believe it. Claudia