I just did try your demo application using Delphi 7. Indeed you have 2 MapPoint instances so that's the reason of view. However I have no idea wy the saveAs not works on the mappoint class.
I just tryed on an older application using a own made component for MapPoint (using Delphi 5) and the SaveAs do not work there also.
Do you really need the SaveAs ? Maybe it is better to save lat/long/alt of the map, including all pushpins etc and reload at next run ? Just a tought as I'm a little out of idea at the moment