Once connection has been published to Tableau Server, it retains the groups, calculated fields, etc as when it was first published. To get groups to update, you'll have to republish the data source and replace the outdated Tableau Server source.
Hope this helps!
I find that best practice is probably to maintain a master TWB file with the original data connection - and re-publish from this master file each time a change to datasource is required.
As an alternative, If you have access to 'DataSources' on Tableau server, you can check the box, and 'Download' and open the TDSX file. Edit the groups as required, and then re-Publish to server.
Of course, need to have a policy on which method you choose, beacuse if you do both, you will lose changes next time the other method is performed.
+1 on Craig's reply