If adjusting the reverse cable doesn't help, check your reverse shift switch on the rear of the engine. It could be going bad or the wire might have a bad connection where it attaches to the shift switch.
Most 4-wheeler problems are caused by a loose nut connecting the handlebars and the seat!!
You only need two tools in life -- WD-40 and duct tape. If it doesn't move and should, use the WD-40. If it shouldn't move and does, use the duct tape.