It is possible that the scale is changing, and you are passing the threshold of the scale range applied to the maps, so you are seeing different basemaps. Try maintaining the same scale, or capture a static snapshot of the basemap to your local drive, and use that. This involves turning off all layers except the basemap in dataview, then choose "Export Map" and select to PNG or TIff, and select "Create World File. You will get a georeferenced image on your local machine, that you can use independant of the image / basemap server.
Regards,
Jim