Unfortunately the seats for a Neon are quite a challenge. I am assuming the seats are bleeding back(lines created by the upholstery tool) or is there a ring on the outer portions of where the stain was? If these are the cases, all that is happening is the extractor is pulling up dirt from the interior of the seat and we need to get all of it out. It would help also if we knew the type of stain( dirt,food,grease etc.)Without knowing the specifics, take some foam cleaner( I use Xtra Duty by CarBrite) apply it to the stain and let it sit for a moment. Agitate with a white terry towel or fabric brush. Then extract. This unfortunately can be time consuming since you will have to wait for it to dry to see the results. May have try again if you notice improvement but not quite all out. If that doesn't work some of my guys will take a solvent(ProSol or even Laquer thinner) apply it to a soft white towel and hand rub it out. Obviously if you use the laquer, do not use too much. We don't want the car to stink. Let me know if those work otherwise there is one more method I can share. Requires an iron though.
Doug