Did you look at: AutoCAD .NET Devemopper's Guide > Control the AutoCAD environment > Create, Open, Save and Close drawings > Create and Close a drawing ?
The Database.Save method is "Not Implemented" at least through 2012. It still says the same thing in the 2013 docs.
You have to use SaveAs, or if the drawing is open in the editor, and you are closing it after, I believe the Document.CloseAndSave method does work. I just searched, and can't find any of my code that uses it, but I think it used it once in the past, but eventually changed that code to work on side databases instead of opening files into the editor.
It is nice as in link to make it an extension method so you can just use Document.Save().