Mystery solved:
I confirmed Mike's results on his computer (apart from the portion about the file needing to be named "OE$INV"). If he specified a filename longer than 8 characters, it wasn't being saved.

After some testing and with help from Mr. Google, I have an explanation for those results: His Windows operating system was configured to NOT track short filenames.

The first thing to know is that Windows keeps space for 2 names for each file. There's the long filename (ie. "OE$Invoice for European orders.dat") which can be up to 255 characters. It also reserves space for the short filename (ie. "OE$INV~1.dat") which is limited to 11 (8 + 3). If the filename exceeds the 8,3 format, Windows saves the long name and but also creates and saves the short name. If the filename already conforms to the 8,3 model, the short name is left blank.

To see this, go to the DOS prompt (File | Run and enter cmd). Move to a folder with long filenames and type DIR /X. You will see the long filenames on the right and a column just to the left with the short names.

If you don't see the short names, Windows has been configured to not track the 8,3 names. Some people disable that feature with the goal of improving performance, though others dispute the effectiveness. Here's an article from Microsoft on how to edit the registry to enable/disable 8,3 naming: Microsoft Tech Note

The reason this matters is that Adagio stores the short filename. This is more efficient than storing 255 characters which would degrade performance. So when Mike selected an invoice layout with a longer name, Adagio picked up the Windows shortname for that file and saved it. The problem was that Windows had only a blank where the short name would normally be located.

For environments configured like Mike's, filenames must be no longer than 8 characters and must not include a space (except at the end: "OE$PICK.dat" is OK but "OE$ PICK.dat" is not).