Hey Gary,
It depends on the way you've integrated TurboActivate into your application. If you're using IsGenuineEx(), and the customer activated online, then yes the customer will need to have internet access every nDaysBetweenChecks.
If you're using IsGenuineEx() and the customer activated offline (http://wyday.com/limelm/help/offline-activation/ ), then the customer will not ever need to be connected to the internet.
You'll have to ask your programmers how they implemented TurboActivate into your app. They can always ask questions here. Also, if you show us a snippet of your code we can help you figure out if there's a problem in the way you're using TurboActivate.
Let me know if that helps.