When using the ArcGIS Server's default PrintingTools service, secured services do not display in the printed map if the custom basemap is shared with Everyone.
Change the sharing settings of the services set as the basemaps to secure (share with Organization, Owners, or Groups). When the custom basemap is secured, other secured layers on the map are successfully displayed when printed. In this example, the Stars_Features layer and map image (custom basemap) are both secured and correctly displayed in the print as shown in the image below.
Share all layers with Everyone. Custom basemaps can be secured or shared with Everyone.
Use a custom print service. All layers are displayed in the print regardless of the sharing settings.
Use Esri's public basemaps instead of custom basemaps.