You are looking at DRM (Digital Rights Management) .. lots of (mega) expensive solutions exist however you need to be clear about what you are trying to achieve if you want to avoid turning your paying customers into non-paying 'pirates' (ever get fed up with being forced to view all that 'FBI warning' and 'coming next' advertising garbage at the start of every commercial DVD ? just get the 'pirate' version) ..
The only 'guaranteed' way is to have the Pi fetch on-the-fly encrypted data from your web-server .. when the time has expired you send a gentle 'reminder' as well (or instead) ... of course the Pi has to 'note' what it's already 'used' once (otherwise you can 'Ground Hog Day' the Pi with a Proxy Server that stores yesterdays data and feeds it to the Pi a second time along with a fake NTP Time stamp that tells the Pi it's yesterday again)
Personally I would just get the customer to sign a 'usage' based Contract - and have the Pi generate 'usage' data which it eMails you on a daily/weekly/monthly basis .. and on which you can base your Invoice....
This changes your mind-set from 'How to stop the customer using the system' into a 'How to encourage the customer to use the system' and that's far far better for your bottom line