Richard,
This time I duplicated your data down to symbology and the database name of GIS and the fact the DBO is the schema owner and not SDE. I also used the same featureLayer name and published it. The only Diffference is I don't have ArcGIS Server 10.1 SP1, I am one 10.2.1 here. Anyway once again I added the map service as a feature type layer in snapshot mode (like you), and it works great in App Builder 3.6 in the Preview tab. I am not sure I can diagnose any further as it seems to be a map service configuration issue on your end. Have you tried to setup the search widget and do a query on this layer?