A lot depends on the brand and type of fusible you are using. Some fusibles are meant to be no-sew, and those usually stick well permanently. Some people have difficulty with fusibles sticking to unwashed fabric, because sometimes the temporary finishes used on fabric interfere with the adhesion process. If the fusible you are using is a sew-on kind, it will last quite awhile without sewing but will likely eventually lose adhesion.
I like Misty Fuse because it does not make the applique stiff. This means you can create a lot of layers with it and still be able to sew them down. Misty Fuse does not come with a paper backing, but you can create one by ironing it between two sheets of parchment paper and then peeling off one sheet while the layers are still warm.
I haven't done layered applique for some time, and it was not with fusible -- rather, with turned under edges using freezer paper, a la one of the Harriet Hargrave methods. When I did that, I sewed each layer to the layer underneath so that when the entire applique was finished, I sewed only the outside outline of the applique to the background fabric; all of the inner pieces were already sewn to each other.