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Open your Template and get rid of your current css link. Reapply your link making sure to use the browse to folder technique. browse to your style sheet (should be in the Templates folder) Here's the important part: select relative to site root instead of relative to document. That does it.
This never happened in DW 4 (whether it's mx or 4 that's actually flawed is arguable) For Templates (not for css to my knowledge) to work Macromedia states explicitly that they need to be linked in this manner and never moved. But DW4 would automatically update the path to your style sheet regardless of what direcory you saved your new document to. One curious thing is that although your document now contains the site root path you can still (at least I can) preview it locally without any problem.