It's not a 'chain' FATE. It just pops....when it wants too. This is a major area of discussion for players doing the 'Beast Tribe Daily' quests - as they potentially require players to complete 1-4 FATEs daily, each of which may take 2+ hr to appear.
I -think- SE increased the pop rate of CT FATEs a while back? Maybe 2.15? or 2.2? Not sure, but I'm pretty sure they 'fixed it'. My advice? Netflix & Chill.