When I set my computer to go to standby, the keyboard lights do remain lit, but that's the only situation where they do, now, which is how I prefer it. Now, when the computer powers off, the keyboard lights do turn off. What I changed to fix it was to simply set it to allow the OS to trigger the state change out of sleep mode. This apparently meant that it would be still feeding power to the keyboard for the purpose of being able to trigger on a key press, and hence the keyboard lights would remain lit, even when powered off. If I launch it by hitting DEL when it's doing its POST, I found that what was set under Power Management was to have it listen for wakeup events from the PS/2 keyboard and have the BIOS trigger the state change. My motherboard is an MSI 890FXA-GD65 AMD Socket AM3 and the CMOS setup utility was made by American Megatrends. I figured out what to do to fix it, though. When I would shut down, the keyboard lights would remain lit.
I have a Das Keyboard which I have plugged into my computer's PS/2 port. I ran into this myself on my new computer that I just built.