I have read at least a dozen posts about Excel data sources not updating. I also read the KB on how to do this.
I struggled with this for a bit and one mention in one of the posts was the key answer. The refresh wasn't happening because the data was cached. Our server is set to Balanced mode to cache for no longer than 120 minute(s). I had thought that on clicking the Refresh button that would invalidate the cache, but maybe not in this setup.
I had written a long post detailing my problem and then hit on the answer. Turns out that some time after 120 minutes, the data refreshed.
It is likely that because of this setup, the client project, the Analytic Workbook, does not impose a cache refresh on the providing project, the Data Source Workbook. I leave here for posterity.