I wouldn't worry about people who uninstall and then reinstall applications to avoid hitting the demo limitations after N days. Folks who are prepared to go to that length to avoid paying a few bucks very likely would never pay - hence no lost sale for you.
What's more, you actually want to allow people to try an application again. For starters, they might run it once to see how it looks and then forget it about -later, when they rediscover it, the period would be over forever - not good. Or they might not like version 1.0, but want to try it again once 1.4 comes out which has the feature they really missed in 1.0.
For all these reasons
you should allow people to re-try an app if they reinstall it.