UPDATE - Want to get around the limit? Just delete the demo and download it again to give yourself another 15 battles!
I sure hope you didn't plan on spending too much time with the Pokken Tournament DX demo. Unfortunately there's a limit to how much you can play it, and that limit sits at a paltry 15 battles. Seems like that could be blown through really quickly. Do your best to have some fun with it while you can!