Warning: contains spoilers for Supergirl: Woman of Tomorrow #8!
Fans have long speculated how Kryptonians like Superman live such long lives, but one scene with Supergirl shined some light on their reported immortality in DC Comics. This happens in the final issue of Supergirl: Woman of Tomorrow. The eight issue series was written by Tom King and illustrated by Bilquis Evely.
The story follows Supergirl as she embarks on a journey with a young girl named Ruthye. They are searching for a man who killed Ruthye's dad and poisoned Supergirl's dog Krypto. The tale is told through Ruthye’s point of view. She uses narration to recall their adventures during some unspecified time in the future. It is only during the series' final issue that it's revealed the narration is actually part of a book Ruthye wrote about her time with Supergirl. Eventually, the pair finds the man they are looking for and decide to send him to the Phantom Zone as punishment.
Decades later, Ruthye, now an old woman, had published her book. She is waiting for Supergirl during the comics’ final pages. Supergirl is coming to see her so that the two of them can retrieve the man from the Phantom Zone together. But when Supergirl arrives she looks almost exactly the same as she did when the two of them went on their adventures. Ruthye had aged from a girl to an elderly woman while Supergirl only aged a few years, if that. She does arrive with a new hairstyle, too, so that might be one reason why she looks a little older, though it’s impossible to tell.
This aging tracks with Superman's appearance in the Future State title, Superman: House of El from Phillip Kennedy Johnson and Scott Godlewski. That story is supposed to take place in the year 3000, but Superman is only a bit older, probably middle-aged. This means that once exposed to a yellow sun, Kryptonians will age normally up to their prime, but the aging process will slow down considerably when their bodies reach a peak level of maturity. They are not immortal per se, but they age so slowly that they may as well be.
Also interestingly, Krypto appears in this final scene as well. Ruthye is happy to see him and not surprised at all that the dog is still alive. This indicates that the Kryptonian aging process extends to animals, too. It's one thing for a human-like Kryptonian to appear immortal. It's another thing for a dog to age the same way when their lifespans are typically a fraction of a human's. Supergirl and her dog are just that inseparable.