Sometimes there can be a tiny burr somewhere along the thread path that causes the thread to be stressed and break. If you can find some sanding thread at a hardware store you can floss along the thread path and that may smooth it out.
I used a lot of monofiliment thread for years on one machine before I realized that it had actually worn a groove in one of my thread guides that was causing other (heavier) threads to break, and I had to replace the last guide before the needle. This is NOT something that most machine techs check for!
You might also want to check your tension. Start with your bobbin tension and then adjust your top tension to get a good stitch. If you aren't sure about adjusting your tension, you will find lots of great information here:
http://www.superiorthreads.com/education/

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