I believe that the idea of blending by peaceful interbreeding is just wishful thinking based on modern ethics.
Some Neanderthals have probably blended into modern human tribes, most likely some children or women. Other hybrid humans may be the result of random encounters.
The majority of the Neanderthals have disappeared during a relatively short time span, of a few thousand years. Some of them might have died as a result of direct fights with the expanding modern humans, the others might have been forced to retreat into worse territories that provided less food, so their population has dwindled.