What causes stitch problems when stitching over fused areas of a quilt?

This could be caused by the brand/type of fusible, but you might also need to check the timing.  If there is contact between the needle and the hook, it can warm your needle slightly (or even sometimes enough to burn your fingers), causing the needle to heat up and melt the fusible, gob up the needle and cause skipped stitches and breaks. Try slowing the machine way down, and check if you using a 4.0 (18) needle with your longarm.  Also, use a needle alignment magnet and make sure the needle is in perfectly straight.

You can check the timing by taking your needle plate off and hand turning the wheel while looking down the side/tip of the needle.  Does the needle tip flex forward at all when the hook comes past it?  If it does flex, your timing needs to be adjusted.  We’ll be posting videos about this soon.
If the timing looks good, it just might be a no-sew type fusible, and you may not be able to stitch over it no matter what you try.  Make sure when you put the plate back on, you drop the needle (hand wheel) in the hole and center the plate before tightening it back down.
So, the best fusible we’ve found?  I only use Heat and Bond Lite, and have had no issues, even when stitching through five layers of batiks and three layers of fusible (even using Bottom Line thread, top and bottom, no less!).  I’ve tried a more expensive brand, but found the edges frayed over time, so go back to my Heat and Bond Lite.  We recommend it to customers, and if they do bring in a quilt made with something else, we let them know that it may not be stitchable.