A few thoughts.
Check your Firewire cable is actually plugged in and properly seated in both your external device and on the Mac. Check the ports inside, are they clean?
Try an alternative cable. Try alternative disk media.
If you have a chain of Firewire devices the devices in the chain must be powered up between the particular external device and the Mac. An intervening unpowered FW device will cut the chain.
Is the cable too long? I think the cable/s max out at 2m.
Possibly Toast is having trouble communicating with the device. I found that it would drop a device sometimes then discover it again. Helps to have a 2nd burner to test this on.
Possibly your CD/DVD drive is having trouble reading your disks. This can be due to condensation or misting up of the heads, or even the heads being damaged. Although the fact that it works with USB seems to rule this out.
Devices do die, I've lost a few burners in my time. Take it to another computer and see if that also has a problem seeing your drive with FW.