So they interbred themselves into extinction, perhaps? Any absorption was like a mop up of the few remaining folk.
One thing I've seen a few paleontologists discuss is that Neanderthals lived in isolated groups with very small interconnections. In contrast as soon as EMH show up they can find trade networks in stone and shells, etc., stretching across hundreds of miles. The fundamental weakness of Neanderthals may have been an inability to form social networks larger than small clans, which might also explain the small populations ad inbreeding.
They’re not extinct, they’re our ancestors.