If you go with a metallic, topstitching or large-eye, (different names for the same style of needle) in the needle size that's correct for your thread, you may have better results. The larger eye causes less abrasion and weakening of the thread.
There may also be defects in the eye of the needle that are shredding your thread, so changing the needle is always something good to try.
Or maybe you're running your machine too fast for the speed at which you're moving the fabric? If your stitches are teeny-tiny, try slowing down the machine or moving your quilt faster to elongate the stitches and use the thread faster.
The thread doesn't go straight from the spool down the path into the fabric - it kind of see-saws through the eye of the needle several times before it gets planted in the fabric.
The smaller the stitches, the more times any given point on the thread is going to get rubbed through the eye of the needle. Use up the thread a little faster with longer stitches and it won't get as much abrasion.
Hope that helps! :)