What is the usefulness of the probability of a user having churned three months after he last visited the system??? There is a method outlined in the article 'Counting Your Customers the easy way: An alternative to the Pareto/NBD model' based on a similar idea, but with much more useful tools and robust mathematics.

Actually, in the post I do mention that I choose months for the analysis, but a more granular view can be chosen, like days or weeks... it might be the case that for the business-model you're interested in, it makes more sense to analyze churn in days - and you can do that! :)

Also, (as an example) in telecom operators for pre-paid customers, you don't know when the user churns because there is no subscription. The method I describe allows us to assign a churn date to customers based on inactivity. You can definitely recover customers who have been inactive for 3 months... although it's less likely than recovering customres inactive for 2 months... etc.