There are a limited number of fates which can be active within a zone at any given time. Thus, if the zone you are in, has a bunch of other fates up, the presence of those fates will prevent the one you want from spawning. Solution, complete the other fates to free up the space. While this will not guarantee that your desired fate will spawn, it increase the spawn rate of it.

Additionally, some fates, are "rare" and have lower spawn rates. The event fates are usually not included in this category. Just providing context for your future in this game when doing things like Relic / Daily Hunts / Beast Tribes and many other activities which involve fates.