Neanderthals were adapted to the cold and for hunting big game, they thrived during the last ice age. As the climate warmed and a lot of big game died out, their physical traits and way of life weren’t as advantageous/sustainable, and for whatever reason they were unable to adapt to keep up with the environmental changes. Competition with early modern humans probably didn’t help, and as some other people mentioned they interbred with early modern humans, so they may have just been gradually absorbed into the human population