Você deve usar a opção de configuração ControlPersist.
ControlPersist
When used in conjunction with ControlMaster, specifies that the
master connection should remain open in the background (waiting
for future client connections) after the initial client connec‐
tion has been closed. If set to “no”, then the master connection
will not be placed into the background, and will close as soon as
the initial client connection is closed. If set to “yes”, then
the master connection will remain in the background indefinitely
(until killed or closed via a mechanism such as the ssh(1) “-O
exit” option). If set to a time in seconds, or a time in any of
the formats documented in sshd_config(5), then the backgrounded
master connection will automatically terminate after it has
remained idle (with no client connections) for the specified
time.
ControlPersist no é o comportamento padrão, que é como você descreve. Eu uso ControlPersist 4h para permitir que as sessões em segundo plano se limpem periodicamente.