My Singer 31-15 skips stitches on curves when the needle clamp isn't adjusted properly. The needle clamp needs to be adjusted to an exact position or she skips. On mine, the screw on the clamp that holds the needle needs to be almost perfectly horizontal, or it will skip stitches on curves. I have learned this after much trial and error.
I have used Essential Pro Polyester Thread from Connecting Threads for several years without any problems.
If you'd like to see my Singer 31-15 set up, you may visit my blog:
http://busyhandsquilts.blogspot.com/...g-machine.html