if you used the no-sew fusible web, maybe you didn't iron it long enough. You should be able to re-touch the edges with the iron. If you used the sewable fusible web, you must sew it down after ironing or it will not stick very long, especially if washed. If you have already started quilting, (actually,sounds like you are almost done quilting.) doing any machine stitching to sew it down is now probably not an option, at least where you have quilted.
Maybe you could handstitch down the edges where you have already quilted. Good luck.