Though a sundry of factors can affect FireWire device visibility, MacFixIt reader John Wong and several others have had success with a simple workaround first posted in the MacFixIt forums that involves simply resetting PRAM, then disconnecting power from the problematic Mac and disconnecting all FIreWire devices (also removed from their external power sources) for a period of time - most successfully overnight.
The original MacFixIt forums post reads:
"Try Zapping the PRAM...if that doesn't do it then turn the power off your Mac, disconnect everything(except the keyboard), including the power cable , leave the power off for 5 minutes, reconnect the power cable and the other cables and restart. Both of the methods worked for me although zapping the PRAM only worked once...the Firewire connections went out again in about a week. However, the second method worked and I have not had further Firewire problems in over a month. My original indications were as if there were no Firewire HD...nothing saw the Firewire HD. "
Subsequently, MacFixIt reader John Wong wrote "Thank you very much for posting your solution to the exact same problem that has dogged me for the past couple of weeks. It worked out great!"
Another MacFixIt reader, Stan, had similar success: "After resetting the PRAM and shutting down for a night, the FireWire drive reappeared on my desktop. [...]
"What was confusing was that the first time I just shut down for several minutes, and it did not work. However, after a night, it did. I am not sure why, but so far, it seems to be OK."
Instructions for resetting PRAM can be found in Knowledge Base article #2238.