Fleece will work AND hold up IF you use a fairly rigid batting between the front and the back. I made a beautiful cover for my window seat and because it wasn't going to be moved around a lot, I just used two layers, the pieced front and fleece for the back. Over time the seams have started to come apart and the entire thing has been pulled a little wonky.
I'll never do anything like that again. My piecing is too special to see it pulled apart by the flexing of the backing. Maybe for a dog blanket or something I perceive as being disposable, but never again on my special quilt tops!