Thanks, Martin, I appreciate your reply!
It doesn't seem to be a permission problem. While I do keep my queries on a shared resource, access to that source is not limited when this occurs (e.g., it works fine in other applications), and I also cannot restore the button functionality by choosing any other save location (such as desktop, My Documents, etc.).
Interestingly, today when I first tried to test the above functionality, the Save As dialog box worked just fine... twice! However, upon going to another open query and doing the same thing, it was back to broken (and was also then broken for the first query attempted).