You can stay connected to several servers at once. The Connection Manager shows your active connections, available access and dependent work. Switching the target in Interwebs does not silently disconnect the previous one.
A window is not a connection
Closing a window or browser does not make your game server leave every remote machine. This matters for both ongoing work and visibility: connected machines can be observed through the game's network tools when the relevant defenses allow it.
Open an existing connection to return to its target. Ninezilla can use your connected servers for file transfers without requiring you to type the same address again.
Disconnect deliberately
If a connection is needed by active tasks, disconnecting shows a warning. Confirming cancels the tasks that depend on it. Other connections and unrelated local work remain separate.
Let a required transfer, scan or remote action finish before disconnecting if you want its result. Pause or cancel controls do not give a task permission to keep working through a disconnected server.
When access changes
A shutdown, changed address or invalid access can break a connection. A saved contact is not proof of a current session. Revisit the target and check the reason rather than repeatedly trying to finish an action that has already been canceled.
IRC also has an explicit disconnect option. Leaving one chat room is different from disconnecting the chat service. See Interwebs and Task Manager for the related views.