Initialization of the data source failed.
Check the database server or contact your database administrator. Make sure the external database is available, and then try the operation again. If you see this message again, create a new data source to connect to the database.
Then you get prompted for credentials, and then get a message about reinstallation of drivers.
There are a few red-herrings in the messages provided by Excel - but the underlying problem in our situation was just a permissions one.
To resolve, you just need to give the end user with the problems permissions to access the SSAS database (e.g. by adding them to the TFSDataReaders role in SSAS). Alternatively, you can add the user as a TFS Administrator in the TFS Administration console (though this is not preferred as it is against the security principle of "least priviledge").
Till next time,