The behavior I've seen is that when you log out, the process doesn't end until all other clients to the connection have exited. I've observed what you describe if I then ^C it.
The way I usually do it is by opening something over TRAMP before opening any other ssh windows. That way, Emacs will handle the connection maintenance and I don't really need to see that it's up. If it dies, I just try saving something and it'll re-establish the connection.
If you don't use Emacs, you can always just start a dummy connection first and minimize/disown it.
There's a good chance I was just doing it wrong™ though.