Is it possible to replace the seat rails on a saddle?
High end saddles like Brooks do offer rail and frame replacements: http://www.brooksengland.com/en_us/spare-parts.html

You might google "yoursaddlecompany rail replacement"

But if your saddle cost less than US$50,
I doubt it is economic to do so. Stocking SKUs and supporting a repair/parts department costs money for the saddle company. 

You're better off either just getting a new saddle or seeing if you can't buy a used saddle with a trashed seat cover and doing a transplant. Note that many saddles are riveted on so this may be a big pain.