I had a similar problem trying to move data sources from a development environment to a production environment. The following thread solved the problem for me:
In addition to those steps, I found that you must also publish the workbook first (with the embedded TDE), and then publish the TDE, and then publish the workbook again with the updated Tableau Server data source (which is now your published TDE). Don’t forget to click ‘Update workbook to use the published data source’.
Probably also worth mentioning; a connection from a workbook to a published TDE elsewhere on the server will show as a LIVE connection. This is a “live” connection to a published TDE. The published TDE can be found under Data Sources within the appropriate Project. If the TDE were embedded within the workbook, it would show as EXTRACT under the workbook data sources.