Apple is amazing, the app store is amazing but I really wish they would allow timed demos for their games. This is one thing that I really think would help sales. Giving people a free sample is a old and effective business practice. Simply you give the person a chance to try what you are offering and they can choose to buy it or not.
On the app store developer's usually release a lite version and then offer a chance to buy the real one. This does work but you have to release two apps and it's a littler more hassle than it is worth. It can be problematic to just re-release a demo app. You have to test it and it takes time. Personally, the way Microsoft runs XBLIG is the best. You get 8 minutes to see if you like and then you can buy it. You also submit only one package. I know that XBLA has demos but in the app store's case it might be easier if there was just one app.
Well the solution is already here and the answer is to design your game so that it is unplayable after a certain amount of time. So here a few tricks that you can do to sell a free game
1. After 8 minutes make the points and the game play less fun. For example you can make the speed of the player and the weapons less effective. If the player then wants those abilities back then they have to pay for the game.
2. Make the points and currency scarce. You can make your game less rewarding if you haven't bought the modifier. This way the player can actually get all of the upgrades in the store.
3. This is kind of a cheap move but you can make a necessary object only purchasable. This way the person has to buy your game if they want to move on.
There are many more ways to get around the time demo. These are just a few ways that you can do it.