"Tramp: Waiting for prompts from remote shell" with sleeping Amazon EC2 instance

[Steinar Bang]

Platform: debian testing
          GNU Emacs 24.3.1 (i486-pc-linux-gnu, GTK+ Version 3.8.4) of 
2013-10-01 on biber, modified by Debian

I have access to an EC2 instance that we put to sleep when it isn't in
use.

I did a dired to the /var/log/elasticsearch directory on that EC2
instance earlier, to read the logs locally in a nice editor.

When the EC2 node was sleeping, everytime I tried to do a dired or
magit-status operation, I got the message:
 Tramp: Waiting for prompts from remote shell
and emacs was hanging, presumably trying to contact a computer that
currently wasn't available.

After I had killed all of the "scp"-something buffers, dired and magit
operation of emacs was back to normal.

I rarely stop or restart my emacs, and I tend to just let the buffers
stay around.

Is there a way to let tramp-related buffers connected to the EC2
instance hang around in emacs without the annoying message popping up
when the EC2 instance is sleeping?

Thanks!