update model prediction for each day closer to the event
I would rephrase the problem into a business problem. I.e., What we are trying to accomplish here.

From the sound of it, it seems like a Churn prediction problem. The article outlines some ideas and potential solutions.

In simpler terms, if the goal is to prevent churn by executing the right marketing messages, etc.


How can we predict the risk of someone leaving? Since you have historic data, it can be a supervised learning algorithm to help you identify such risk.
What other features do we want to add to the model? Actions / usage data / web visitation / email open, etc. leading to the renewal days. You can normalize the data by the days prior to renewal, etc.
Determine what actions you want to take; it will help you determine if you want to get a risk score, or a classifier with differing level of risk, etc.