Disconnection Problem Tech support says they never heard of.

[Sarick]

well. maybe you have one of those green power supplies or ups that have a switch or device connected to it on the green port. When you turn it off the port shuts off device.

The TV could also be disrupting the connection when it shuts off IE power spike or electronic radiation. On a final note, It could be the screen saver or software conflicting with final fantasy. When you turn your PC TV off that software or driver loads and shuts down FFXI. If I recall a specific anti-virus software did this every Friday at 9-8. There are some programs trojan software that load when the screen is turned off or the human input devices are inactive (mouse keyboard joystick). They do this to hide activities or do actions while the user is away. It could even be the firewall software or hardware setup shutting down internet when turn off the tv. With these new computers you never know how the power saving works.