So while a Gibraltar Neanderthal sect never made it to the Neanderthal Disney on the Black Sea, maybe there was still just enough ritual travel to, say, pre-historic Gaul to keep the bloodlines from producing a one-eyed Centaur. Maybe.
Think of them as medieval monastery sects. Well, those relied on one another, and when a sufficient number in the network failed or were overrun, so did the whole.
My personal belief is that they were intentionally snuffed out by Cro-magnon in some 500-year event, for their treasure, their locales/caves, and the elimination of competition.
The fact that most people carry DNA found in the relatively few Neander-samples means, they are our among our honored ancestors. Period.