What exactly is a stored display? Is it a map file (.mxd) stored in a database table?
A stored display encapsulates only a part of what is in an ArcGIS map file. An .mxd map file stores information regarding some ArcMap settings, printing preferences/markups/layouts, one or more data frames, user-authored meta-data, and most-recently-used information, among other things.
An ArcFM Stored display is more analogous to a single data frame (more specifically, a single ArcObjects IMap instance), although other types of information are stored within it as well. While additional information or content can be created from the data frame saved in the Stored Display, data such as the arrangement of the page layout will not be saved with the stored display, and if not saved in another medium, will be lost after ArcMap is closed. Additional data frames and their settings will not be saved within a stored display either.
To more closely match the functionality of an .mxd map file, try using a ArcFM Stored Document. While a Stored Document is still not an .mxd file, the functionality will more closely approximate one.