I have had this happen twice since I've owned the Aivia Osmium, but on all other occasions the backlight has switched off automatically. Most motherboards still provide power to USB when switched off to support wake from USB. However I think the keyboard should be able to detect the shutdown and switch off the backlight. It would seem that, depending on your system/configuration, this does not always happen. On at least one of the occasions it happened to me, Windows was installing updates during the shutdown, which may be a factor.
My previous backlit keyboard, the BlackWidow Ultimate, never left the backlit on and so it would seem that the issue is with the shutdown logic/detection on the Gigabyte. When it happens the only workarounds are; switch of your PC at the PSU or socket, or to disconnect and reconnect the keyboard.
Hopefully this can be fixed with a firmware update. Do Gigabyte tech support read this forum?