The torque of the starter will loosten the prop nut- this is not unusual. As the previous posts said, tighten that nut down really well. Also, the reason a nylon (plastic) prop helps keep the nut from coming loose is that it does not crush down when you tighten the nut, unlike a wooden prop. That's the main reason I don't use wooden props.

Another thing that will help is to put a small piece of sandpaper between the spinner backplate and the prop. This will keep the prop from slipping. Just glue two pieces of sandpaper paper side to paper side, cut a hole in the center, and put it on the prop shaft between the backplate and the prop. It also helps keep the prop from moving while you tighten the nut.