If the fabric is just coming loose from your satin stitching, but the rest of the quilt is still okay, what about just cutting away the applique fabric and letting the satin stitch be kind of an embroidery design on the quilt? This would be an easy fix to keeping it from looking raggedy. (I am assuming, from the way you talk about the quilt, it is not destined to be a family heirloom, but more of a utility quilt.)