I use the satin stitch all the time with my applique, never had one fall off. Are you doing raw edge applique... I rarely do it that way, I usually put an interfacing on the back (sew right sides together, cut small slit in interfacing and turn the piece right side out). If you are using raw edge, maybe it is the fabric that is giving away, not the satin stitch. Try sewing a straight stitch around just inside the edge of the fabric.