Color me confused. IIRC, when I was in school Neanderthals were considered a sub-species, not a separate species, which meant interbreeding was possible and likely. Even if a time split between the two groups made interbreeding unlikely (which one of my old profs argued would have made the Nees a separate species), what physiological difference/s could there have been in the Nees that would have made a union between members of the two groups sterile? I thought the Nees were considered a sub-species?
PS. Also the fact that Neanderthal & Cro-Magnon were contemporaries added to the reasons why they were thought sub-species, and to be sure, still are in a sense. Or, to be more precise, their status is currently indecisive between a sub-species or a fully distinct species. However, one thing that is now much, much clearer that it was just a decade ago is that Neanderthal and Cro-Magnon behavior was far more different than had been thought the case. The Neanderthal had inferior tools, inferior weapons, inferior artistry, etc.
"The fact that neanderthals disappear in Europe, about the same time as modern Homo sapiens appear, could be used as evidence to support the replacement hypothesis. However, not all the evidence, however, supports the Replacement Hypothesis in Europe. In 1998 at the Lagar Velho site in Portugal, the remains of a child, aged 3-1/2 to 5 years was found that apparently shows a "mixing" of Neanderthal and Modern human traits. The skull of this specimen has a pronounced chin, which is a hallmark of modern homo, however, post-cranially, the boy's bones were quite robust, and he was barrel chested and had short lower limbs, all of which are cold adaptations which characterized Neanderthal. "From here.
If we did not, in fact, interbreed with them, it might have been a chromosomal incompatability (the evidence is the last common ancestor we shared with them lived between 500,000 and 850,000 years ago) or an anatomic issue.