Disonnected Sessions

When I get inadvertently disconnected, often my sessions will be unavailable
to reconnect when I get back later that day or even a day or so after. But
they will then become available to reconnect a day or few later (so they
were not gone and the remote host server probably did not reboot).

Please, can anyone say, why do they go and why do they come back?

Also, one of my remote W2003 servers gives me Shutdown and Restart as
shutdown options; another one only gives me Disconnect and Logoff. I have
admin rights on both machines. How do I set the shutdown options, please?

Kind regards,
mike K