They have not always been separate species:
- Neanderthals split circa 500,000 years ago when a group moved to Europe where they have been trapped there by glaciations.
Since then, they were genetically isolated from the rest of humans, they gradually drifted apart, especially adapting to cold climate (stocky body shape, more carnivorous diet...).
- 120 to 100,000 years ago, thanks to previous climate warming, our two yet subspecies could move again and meet in Near-East. we weren't totally separated species, and interbreedings did occur. Our 2 to 4 % Neanderthal DNA came from this period.
After this "Eemian" interglacial, central and western European Neanderthals have once again been isolated by the last glaciation.
- 40,000 years ago, anatomically modern humans entered in glacial Europe and met Neanderthals again for a 10,000 years cohabitation. Those were genetically more drifted than last time (more time to drift, more distance and so less contact with Near-East hybridized Neanderthals...).
Hybrids of this period are rare, look weak and sickly or dead at a young age.
That's why late Neanderthals are considered a separate species, not a subspecies anymore.