Controversy around why the neanderthal went extinct exists for a while now. I think it is very unlikely that a successful human-like species goes extinct without a fight. They where stronger and bigger then homo sapiens. If it is true that they replaced homo sapiens as the dominant species for a while then maybe they are not the friendly giants they are thought to be. Even homo sapiens cannibalize, so that some physically stronger Neanderthals would also do this seems not unlikely.
The last neanderthals might have lived in relic populations in north eurasia until several thousand years ago without leaving much archeological evidence. Also oral traditions might survive for very very long. But yeah, maybe it is not so politically correct to 'talk bad' about a race that fell victim to genocide. We rather focus on the positive things about them.