Are you using a zig-zag stitch? Lengthen the stitch length a little. You can also use some tear away stabilizer under the applique and backing. You just float it underneath both layers.
Do you have other decorative stitches on your machine. I don't use the exact zig-zag stitch. I have a stitch that takes the zag on a little angle. I have used invisible thread or just match the color.