Usually I do a release upgrade over the network, using ssh with the command

do-release-upgrade

For some reasons the connection to the host I’m upgrading dies.

No panic. Reconnect to the host with ssh. If it does not work, try port 1022.

Then execute the following command:

screen -ls

here is a screen on:
    root/1234.ubuntu-release-upgrade-screen-window   (09/15/2014 07:48:02 AM)    (Detached)
1 Socket in /var/run/screen/S-root.

Now try to reconnect with

screen -d -r root/1234.ubuntu-release-upgrade-screen-window

The connection is established again and you can continue where you were.