At EmbLibrary, there are really good free instructions for sewing on leather. (There are lots of good embroidery how-to instructions on the Projects page.) I put both links below. Your design may be too dense, not allowing the leather to stay connected under the stitching - like doing greeting cards.
belle, are you using a leather needle? Perhaps the leather is too thick for this sort of sewing or you need to use a WSS topping.