One analyst suggested it's almost as though a female gave birth to cubs deep in a den while all the world above was destroyed along with the Cheetahs running around. A massive widespread tsunami would do the trick every single time (provided these animals preferred very flat alluvial plains for their habitat).
I have read about the evidence for the Cheetah going through a genetic bottleneck, as well.
It accounts for their extreme photogenic appeal, in that they are virtually identical and make fascinating group photos.