Neanderthal had a beginning and ending.
My theory on the ending? I think they were mostly groups/clans....who stayed within their group, and inter-bred. So every two or three generations....their IQ level and health declined five percent (minimum).
So around 30k to 40k years ago....as each clan downsized in population (due to health/dimwittedness).....they went extinct.
A few mingled with the modern-human 'series' and kept some of the dna-pool 'alive' but it was an abrupt end for the Neanderthal.