Dark Eldar suffer from The Thirst, a need to drink the souls of other beings. This rejuvination also reverses aging, so as long as they keep devouring enough souls the Dark Eldar in question is functionally immortal. This means that if they don't have enough souls they'll eventually die of old age, but are more likely to do so before this happens in frantic and deadly attempts to get souls.
Asdrubael Vect, the de facto leader of the Dark Eldar (and the inventor of the phrase, Eladrith Ynneas) is one of the few remaining beings who were around near the Fall of the Eldar in M30, effectively making him over 10.000 years old. Whether this is true or not is uncertain: this claim comes from the story called The Torturer's Tale where he tells his story to a human slave (because he claims that stories are meant to be told and all Dark Eldar already know it).
Mandrakes are a particular case: they have mysterious powers that not even other Dark Eldar understand. Perhaps they're some kind of Psyker, perhaps a mix of Eldar and Demon, or perhaps they're living manifestations of shadows. This might very well mean they're completely immortal, or they don't need souls, or they're out of reach for Slaanesh. Nobody knows for sure.
Dark Eldar can with enough souls live for very long times, but it's unlikely that they do: as a member of a race that involves so many backstabbings that is described best as Revolver Ocelot multiplied by Petyr Baelish one has to be extremely brutal and cunning to survive, and one mistake sends you over to the banquet of She Who Thirsts. Only Vect managed to do that so far, and anyone else who got close to getting as old as Vect will inevitably get into conflict with him and fail. Even with cloning technology made possible by the Haemonculi, you'll die when you have your soul devoured.
To add, while the Dark Eldar are stronger and more agile than the Craftworld Eldar their less crazy cousins can become just as old: Eldrad Ulthran was already a Farseer when he spoke with Fulgrim during the Great Crusade, meaning he's possibly older than Vect is. Though much like for their darker cousins the Craftworld Eldar do not often reach such venerable ages: they die in combat and that's it for them. But they have their soulstones, and by adding these to a Craftworld's Infinity Circuit the spirits of the Eldar can live on inside the Craftworld, meaning there are souls in there who have been so for millenia.