By persistent I assume you mean we have never seen one of them stop functioning.
We only found them, what, twenty years ago and we have identified, how many?
Theoretically there are billions of them and each galaxy has a huge BH at it's center.
Having only learned of their existence a couple of decades ago, we can't say much about their persistence, cosmologically speaking.
In case I somehow missed your point, my imaginative theory is that not all black holes collect sufficient mass to create a big bang. Perhaps only the galaxy center black holes. I have no theory on how long it takes. Time is always on the side of cosmic incidents.