Generally we only get "staining" by leaving it on the mat for a week or more instead of wiping it off. BUT, time and repeated wiping with water simply in the normal course of continued use gets rid of them.
Which gets to the other key way to avoid staining a battlemat -- don't leave marks on it. Always clean it off at the end of the game session. I've found that marks left on, even overnight, are much harder to remove.
