Are you using manually scheduled tasks in Project 2010? Is your calculation set to manual? For manual scheduling check the "task mode" field. For calculation, see if F9 updates the data -- if so, likely your calculation mode is set to manual. Go to File > Options, Schedule, Calculation.
The other reason why dates stop responding is having Actual Start and Actual Finish dates. Apply the Tracking table to see if you have Actual Start and/or Actual Finish dates.
Julie