Are you using a live connection in the workbook for connecting to the excel on the network drive if so try converting it into an extract and it should work. Hope this helps and let us know the update.
I think you are probably just including the Excel workbook during your publish. You may think you're live, but you're not.
When you publish, make sure you de-select the Include External Files option at the very bottom of the dialog, then see what happens.
Yay. Thanks, Christopher. (And Venkata.) Christopher, your response makes complete sense. I do, however, find the whole connection to data sources a massively frustrating and confusing part of Tableau.
I'll give your suggestion a whirl and see what happens. Much obliged.