Hello,
There were known issues with tagfield, pagefield, and pathfield components in the multifield.
The fix has been backported to 6.3.3.0 as part of NPR-24177.
You can search for "NPR-24177: Hotfix for Granite-21548" here, and verify the fix in SP3:
https://helpx.adobe.com/experience-manager/6-3/release-notes/sp3-release-notes.html
Please install SP3 or latest CFP and check again.
Also, do you see any error in the browser console while saving the dialog?
Regards,
Vishu