Are you trying to clear other FATEs in the zone while you're waiting? That can help get the one you need to spawn. If other FATEs aren't being cleared it will take that much longer for the one you need to have a chance to spawn.

But as dspguy asks, do you really need to do that FATE? The ARR hunt bills aren't the best design and Allied Seals aren't the most useful to max level characters. I just do the weekly ARR B rank bill and the occasional S rank. Eventually I get to the point where I cap and dump a bunch of the seals into Aetheryte tickets (which I also have far more than I use).

If you mention why you're specifically going after Allied Seals, perhaps we can suggest better ways to accomplish your goal.