Very odd. I haven't used the Duet myself but there are plenty of user reports which suggest that the device works just fine with the VO Tool in FCP (but only with Mic Input 1 as I advised above). There are many other FireWire based Mic interfaces that also work just fine, so it's certainly not a FireWire thing. I can only suggest that, having plugged the Mic into Input 1 you recheck all your settings, on/off switches etc and make sure all is absolutely as it should be.
Another option for you would be to set up an Audio Only capture preset, and record your voice using Log and Capture:
Go to your FCP Audio/Video Settings... window (Cmd - Opt - Q) and switch to the Capture Presets tab
Select any capture preset and press the Duplicate button.
In the subsequent Capture Preset Editor window:
Set the Name and Description to Apogee Duet - Audio Only
Set the Quicktime Video Settings >> Digitizer to None
Set the Quicktime Audio Settings >> Device to Duet, Format to 48 kHz
and then press OK
Now open your Log and Capture window and switch to the Capture Settings tab
From the Device Control popup select Non-Controllable Device
and from the Capture/Input popup select Apogee Duet - Audio Only
Now switch to the Clip Settings tab and uncheck the Video checkbox (leave Audio checked).
If everything is working you should see the levels jumping in the Clip Settings audio meter when you speak into the Duet attached Mic.
If so, click Capture Now and away you go. In future you should just be able to easily access the Apogee Duet - Audio Onlycapture preset as and when needed.
Maybe that will work for you.
Hope it helps
Andy