It used to be that when you downloaded a game demo, you were free to play it for as long as you wished. Often demos only consisted of a single level or mission, just enough to give a basic idea of the game.
However, lately game demos have become increasingly absent, especially when it comes to much anticipated AAA games. Publishers are free to offer game demos on the Wii U eShop, but they are also free to limit how many times players can enjoy a demo.
This is the case with demos in the 3DS eShop, and the very first demo on the Wii U eShop, FIFA 13 from EA Sports, has a play limit of 10 times. Which means the demo/software can only be launched 10 times, whereafter access to it will be blocked. Re-downloading the demo won’t help, though, as the limit is set per-account.
It’s likely that Nintendo will offer the same freedom to publishers as they do on the 3DS, where game demos have limits anywhere from 5 to 25 times. But most demos have the limit set at 10 times, which should be enough for any player to decide whether he wishes to buy the full game or not.