If the company has documentation to back up their side - something like "he/she was found asleep at his desk several times (dates A, B, C), was given both verbal (on date D) and written (on date E) reprimands, continued to sleep at his/her desk (dates F and G), and was let go on date H" - then I don't believe that there's a law that stops them from doing so.

Yes, they may get sued - but they're likely to win the lawsuit (especially if they required the employee to sign the written warning, so he/she can't claim ignorance).