Are you using Live Preview, or Open in Browser?
Live Preview took over the F12 shortcut from the old Preview in Browser. It uses Adobe's servers to give you a live view of your page during editing. Because of that, certain links just don't ever seem to work right. It never works correctly for me, so I use the other option.
You may get more mileage from using the Open in Browser function. You can right click the file name in the Files window, or if your open documents are set as tabs across your App Frame you can right click on the document tab itself, and choose "Open In Browser" which is the old Preview in Browser.
Personally, I dislike Live Preview so much, I modified one of the program files to force DW to use Open in Browser on F12 (since the program doesn't allow remapping that in keyboard shortcuts).