I think what you are doing is saving the .dxf file but not the .dwg file. That is why Autocad is asking you if you want to save. When you click yes, do a file->save and name the drawing. It will be saved as a .dwg file.
If the .dxf is saved, you can import it back into autocad (using the "dxfin" command). Then you can save the .dwg (the native Autocad file).