The point where someone's reputation is tarnished for good. Similar to the event horizon of a black hole (once it's crossed, nothing can escape the hole's gravitational pull, not even light itself), it is no longer possible for someone past the abyss to restore their reputation. If they try to, they will be shunned, ignored, or otherwise prevented from succeeding. If they do manage to restore their reputation, that means they never actually crossed it in the first place.
I think O.J. Simpson crossed the reputation abyss when he was suspected of murdering his wife and her friend. Despite his acquittal, his reputation was irreparably damaged.