Daryl,the fact that they were around for 3-400,000 years would argue against a sudden genetic problem wiping out a very widespread species. I am inclined to agree with Canvasback: throughout prehistory, when H. sapiens showed up anywhere, the large animals soon disappeared (the exception was Africa, where animals had time to co-evolve with hunting humans and develop appropriate antipredator responses). My bet is that H. sapiens simply killed off H. neanderthalensis the way we did nearly all other big stuff around the world. The domestication of dogs might have been a factor, as they dramatically changed human hunting (and presumably raiding) dynamics.