It appears that there is a problem in the Acad .Net assemblies that doesn't work all the time when trying to use the SaveAs method on a Database. The problem is with calling the method like
Db.SaveAs( path, DwgVersion.Current );
To fix the issue I had, I had to call it like
Db.SaveAs( path, true, DwgVersion.Current, Db.SecurityParameters );
Problem was confirmed by this page, which also supplied the solution:
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http://www.private.peterlink.ru/poleshchuk/cad/2009/Bug2apie.htm ]