Yeah, that session will only live for as long as you stay on that panel. Good for short things, but not for any task that might take some time.
If you need to keep longer running operations open, you can open a shell in a new window by selecting the node in the tree view to the left and then clicking on the "Shell" button in the top right, next to the shutdown and power off buttons or by right-clicking on the node in the tree view.
Alternatively a direct SSH session of course.
If you start the update installation in the "Updates" panel, it will also open the shell in a new window.
One other thing that can help you on even longer running tasks or if you do have a spotty connection, is to use
tmux (needs to be installed) as you can detach from a session and reattach to it at a later time.
This feature singlehandedly forced me to reinstall the server. Why such feature?
I believe a full reinstall could have been avoided. You might have had to kill the apt process and run a
dpkg-reconfigure -a afterwards (running
apt-get dist-upgrade would tell you if needed), but it should be possible to recover from such a situation.