Adding a basemap to a stored display may change the current coordinate system of the data frame to WGS 1984 Web Mercator (auxiliary sphere).
This behavior occurs when you use the 'Add Basemap' command.
This issue may be related to one of the following Esri bugs, fixed in ArcGIS 10.1 SP1:
NIM081408 and NIM081490 - Adding a basemap changes the coordinate system to WGS 1984 Web Mercator (auxiliary sphere).
Change the current coordinate system back to the correct spatial reference.
See the following Esri technical article for information on how to update the coordinate system in Data Frame Properties.