At beginning of a block......fold a small piece of fabric (2" square??) and start your sewing in the middle of that, then chain stitch into your block.
Have you cleaned out the bobbin area and the feed dog area lately??? I'm not sure, but the feed dogs stopping working in the middle of your seam........hmmmmmm seems like that's something for the repairman if you've cleaned out the lint, etc.....never heard of it happening. Maybe someone else knows.