They found that the fossil was 39,700 years old, which implies that Neanderthals did not survive at the cave site beyond this time.

Hm. I seem to recall another child Neanderthal from Gibraltar... from 2006:

BBC NEWS | Science/Nature | Neanderthals' 'last rock refuge'

A study in Nature magazine suggests the species may have lived in Gorham's Cave on Gibraltar up to 24,000 years ago.

...The earliest samples of charcoal date to 33,000 years ago, while the youngest date to 24,000 years ago - much more recent than anyone could have imagined.

But evidence for a presence 24,000 years ago is limited, so the researchers can only say with confidence that Neanderthals were in the cave until 28,000 years ago.