Neandertals apparently were a small and widely scattered population, at least according to a paper whose abstract appeared in Dieneke's Anthropology blog. I don't find this blog as useful for Neandernews(or other news about human evolution, for that matter; Dienekes sees more separateness between even "modern" human populations than I do. But from time to time, he collects things like this.
I've suspected for some time that part of the reason the Neandertals disappeared as a distinct type was simply that there were never very many of them. At least one other worker that I know of, feels the same way, but despite this, the person I'm thinking of, doesn't see as much separation between Neandertals and "moderns" as Dienekes does, either.
BE that as it may, their existence was mostly "on the edge", because their populations apparently were quite small. However, a small population or populations, though it tends to work against genetic diversity, also suggested in the paper Dienekes abstracted from, it doesn't preclude at least some. And I hasten to emphasize that, at least for me, they were more "like" us, than different, which is one of the unstated premises of my Great Science Fiction Masterpieces With Neandertals. And for anyone interested in such things, there has long been a suspicion that Neandertals had as much "cultural capacity" as anybody else in their situation. In fact, a man named Brian Hayden wrote a long, but quite interesting academic paper called Cultural Capacities of Neandertals, way back in 1993. It's a bit out of date by now, but the basics probably still hold; for those interested, you can find it in the Journal of Human Evolution, vol 34, pp 114-144(if I've cited this wrong, let me know, and I'll correct it at once)
In any case, small populations are more vulnerable to disaster and catastrophe of one kind or another, than larger ones, and Neandertals seem to have been very vulnerable. While it doesn't look as though they left any genetic imprint on anyone, you have to remember that a small, scattered population may just end up being absorbed at times by a larger one. It also looks as though "modern" human Paleolithic "foragers"(as "hunter-gatherers" are now called in anthropological circles), may themselves have been similarly absorbed by Neolithic farmers, so the chances of some tiny population last living some 30,000 years ago, in cold, Ice-Age Eurasia, is statistically rather slim. Still, this study is interesting because it seems to show what can be done with the genetic material we have, from some of these long-gone populations.