My daughter's 04 had the same problem. Changed the sender and it was good for about 8 months.
It just started doing it again so I guess it need's to be replaced again but thinking of putting in a mechanical gauge. On a different note regarding Neon's, her's will stall on occasion when she turns her defroster on. Of course I have not been able to get it to do it when I try. It started shortly after I replaced the eng. cooling fan assy. with a new one from NAPA. Any Idea's?