TFS will not automatically update one Work Item when a linked item changes. There is no functionality for that out-of-the-box. What you can do is configure an alert.
Or you can test whether the TFS Aggregator that exists for TSF 2010 (open source project) will work for 2012 (not officially supported). It can update child or parent work items when a workitem in the hierarchy changes.
What you want is not possible in TFS out of the box, but you can implement this with relative ease using a custom ISubscriber
or a SOAP webservice. See the following answer on question regarding this.