Nolan's right. Whoever contributed the effects track did it as a mono track shared between left and right, but did it with one of the two electrically out of phase with the other. As long as you listen to the show in full stereo, the effects track will be there although if you listen carefully with headphones, it will sound funny and "like it's coming from behind you."
The minute you mix the show to mono, it electrically adds the left and right sound to each other. Since one of the effects tracks (left) is mirror-image of the other (right), it vanishes.
If the effects are part of the completed sound mix, you're kind of dead in the water. There's no way to fix this in post. If the show is ever broadcast to my house, I won't hear the effects track at all because I listen on a mono sound TV.
One of the classic ways this happens is an error in the way an original analog effects recording was digitized. Broadcast analog audio is easy to mess up this way and is one of the reasons large sound houses have meters that detect this. Sound editing programs can fix this easily, but I don't know if FCP has the ability to flip one track. You still can't fix it once it's part of a healthy mix. You can only fix it if you have the efftects track available by itself.
Koz