[Hampshire] Hibernating X sessions

Hi,

I would like a feature whereby I am running a remote X session to a server.
Then, if I hibernate the local PC, I would like the X sessions to
still be there when I come back out of hibernation.
Unfortunately, the remote machine has disconnected me in the mean
time. We have tried VNC, but it does not seem good enough as it seems
to always only show the console, so not much use in a multi-user
environment.
I thought NX might have helped, but it does not seem to.

A system that does seem to work quite well, as an example, is
remote-desktop to a windows server. With that, one can decide whether
to leave the session open on the server and let you come back later,
or instead log out.

Is there anything in Linux that would give me this feature.

Kind Regards

James