If your stain is actually an attack of the clear plastic and it's in deep then I don't think anything can actually remove it without the product or your excessive rubbing doing additional damage. However, here's two products that I've used on my plastic windows.
Plexus is a good cleaner that does an excellant job of removing salt residues, bird crap, greases, and most other types of dirt without damaging your plastic.
Since my boats canvas and plastic windows are pretty old, the windows have been scratched and turned hazy over the years from using boat brushes and such. A couple of years ago I used a product from Meguirs called PlastX that did a pretty good job. Make sure you use it on both the outside and inside. When I first used it I used it only on the outside, thinking that's where the scratches where. After the first application (on the outside) it looked pretty good. I thought I had missed some spots so I did a second application (on the outside) with no improvement. Then it dawned on me, there could be scratches on the inside. Duh......
As I recall, it also stated it would remove stains as well. No stains, so I can't really speak to that but for about $6 it's worth a shot. But, like I said, if the stains in deep,it probably won't remove it.
It's not the best cleaner however, so I'd suggest using the Plexus first and then follow it up with the PlastX. You definately want to make sure the surface is as clean as posible before you use it cause any sand/dirt will act as an abrassive and scratch the surface. The literature I've read on this product indicated that although it is a polish, the abrassive paticles break-down with continued use (polishing) acting more like using finer and finer rubbing compounds or sandpaper. Try using it with that powerball attachment for your drill. Just be carefull with your pressure and multiple applications as it is a pollish and works by micro abrading. The more pressure and application of the product you use, the more surface layers of plastic you remove.
And did I mention, make sure your surface and aplicator is clean.