They probably did not “just go away”.
SunkenCiv has repeatedly posted the book by Firestone, et al, about a giant extraterrestrial air burst that probably destroyed the Clovis culture, killed most of the large mammals so that they went extinct not long afterward, and created the Carolina Bays. It is fascinating reading, and I am inclined to believe the hypothesis.
I read the book and that is exactly I meant. Even though the three strike theory beginning 41kya is a bit convoluted it is obvious that something really bad happened 13kya which quickly removed Clovis Man and the mega fauna from the scene.