Here is one potential approach. Keep in mind the most suitable solution depends on what triggers your reference date (entered manually, pulled from database, event triggered using web services, et cetera).
Add a new field named DueDate, type date only
Add a Wait shape, then a Send email shape
Switch to Dev Studio, and click on your Wait shape (you need access to the advanced configuration)
Select Reference date/time, and copy/paste the following line
The wait shape will make sure your case continues only 7 days days before your due date, in which case a notification will be sent.