I haven't kept track of time but I have kept an approximate count of FATES completed while wearing a Zenith weapon. Over 800 fates complete and 4 stones to show for it.
Since it takes approximately 3 minutes crush a fate and 2 more minutes to wait for the next fate to popup, I have been farming approximately 11 fates per hour. So, 800 / 11 = 72 Hours give or take.
RNG is hell, when the dice always comes up snake eyes.

The drop rate is going to be doubled in the next patch, hopefully my luck will turn soon.