do all the above (smaller, sharper needle, thinner thread (should be 50wt, but try 70wt if needle is tiny, hold thread). Also keep single hole plate, and don't use a zig zag foot. Use a straight stitch foot).
If all else fails, buy a machine with the feed dogs close together. Modern machines often have feed dogs far apart to deal with decorative stitches and wide zig zags. This is the main reason I piece on a Singer feather weight.....to stop the machine from eating my fabric at the start stitch........Jane