You could try a different machine if you have something to choose from. Like nabobw says, rayon tend to break more easily, but you should be able to stitch with it. Be very fuzzy about needle (large enough or just a bit larger than strictly necessary). I have managed to free motion and top stitch on an vintage singer with shiny rayon thread, it's a very basic straight stitcher (201), and I imagine any machine should be up to it.