How to keep your chat room open
In general, your chat room is free. It can stay open and visible on the list as long as you or your at least one of your chosen admins is in the room. If you have enough admins, you can keep the room open indefinitely.
If you do not have a paid room, if no admins are present in the room it will not be listed.
If you have a paid Ultimate or Elite room, there is a special setting in your group setup area under the 'premium room settings' tab. You can enable the 'show my chat room in the rooms browser even when empty' setting that will keep it open regardless of the presence of your room admins.