I just did this quest last night. Decided to try the one by Camp Bronze Lake in Upper La Noscea, and the FATE popped within a couple minutes of showing up. But that's just my case. Anyway yeah, like the others said, if it's taking a while you can try beating other FATEs until it comes up (more gil and XP!). I also suggest bringing out your chocobo to help out, if you've unlocked the ability to have it fight with you. Good luck!