The solution is to use custom license fields. For example, create a "subscription_expires" field, set it to when the customer's subscription expires, and read that value in your app after you request a lease from the TurboFloat Server. If the date in "subscription_expires" has passed, then you can just tell the customer from within your app, to renew their subscription with you.
And of course, you can update that "subscription_expires" field value.
Does that make sense?