Execute a rule after a countdown finishes
You need to use Rules Scheduler. You can create a date field on you content type, and then on some event such as creating or updating the content type you :


check for an old scheduled event on that content instance and delete it 
read in the date field.  
schedule a new event.


The event that you schedule will be a rules component that you create that will take in the nid of the content type, and then in its action section closes it.

If you need help on this check out Johan Falk from Node One's series on Rules.