I have seen some users asking this query on the internet. Currently, Revit does not update Door's From/To room information in a door schedule if you flip door in the plan view. However, there is a work around to deal with this. Please see Steve Stafford's recent post about this work around.
This behavior is intentional. However if you want to update all doors from/to room information automatically then use the following tool.
***Update 24/06/2013: Visit DOWNLOAD page to download this tool.