As I have stated if Neanderthal societies interbred with Humans and had viable offspring the societies died only because they gradually became Human societies (this is especially true if Neanderthal is simply a cold adapted Homo Sapien). This could happen in as little as two generations and leave almost no evidence other than Humans now living where Neanderthals once lived. These societies die out because the new children are brighter and faster than their parents and would out compete their companions for food, sex, and control. Homo Sapiens are just more capable than the cold adapted Neanderthal.
As I already stated above, you are perfectly free to imagine any scenario you want so long as it would leave behind no evidence. For what little my opinion matters, I have no problem with that so long as you don't claim that there's evidence of scenarios that produce no evidence.