You don't have to ungroup; if the old tag manager broke down you just unplug it and the "server-room" tag manager you showed will keep working in place of the old tag manager. If you ungroup, you must unassociate all tags and reassociate, and you will lose the event history (temperature/humidity data can be migrated to a new tag by the Setting->Move Data feature though).
Ungrouping a tag manager involves copy its serial # into clipboard, delete it, click save, then open the account screen again, add a new tag manager, and paste the serial#, do not check group option. This is not that obvious so we plan to add the "ungroup" option on the "Edit" menu next to each tag manager in near future.