Before I take a stab at answering this I have a few questions:
When you are referring to the old completed task, do you mean the completed subtask?
Do you need the subtasks also to have a date? Or could you be content with the main task being the only one having a date?
A limitation of Asana currently that we’re going to have to work with is that recurring tasks do not trigger rules. If you feel this helps adding your vote and voice to this topic is appreciated:
I think the issue was that I multi-homed the task into the Project ‘Operations.’ Thus, when a new task was triggered for the next day, it added the next day’s task to the Project and kept the old one there!
I have now discounted these multi-homed links and built them in each main project where they should sit.
FYI: If you have the license for it you can put these automations in a bundle. Rules in bundles will only fire once per task even if the task is multihomed into multiple projects that have this bundle.