I have a WD TV Live with the latest firmware (1.02.21) and a WD20EARS in a Vantec Nexstar 3 enclosure. When I power off the WD TV, the USB drive stays on. In fact, the light indicating drive activity on the front stays on.
When the USB enclosure is connected to Windows 7, the drive properly goes to sleep (powers down) when not in use. But when connected to the WD TV, the drive is always on.
Have you tried “Eject”-ing the drive via the remote prior to turning off the Live?
Another option would be to unplug the power from the Live; it seems like when the unit is turned ‘off’ via the remote, it’s really in a slightly active standby mode, hence attached devices not registering that they should power down.