In some versions of the mythos, Amazons are immortal, and already several thousand years old by the time Steve Trevor lands on the island in World War II.
In some versions, the immortality only lasts while they are on Paradise Island. In this version, Wonder Woman ages normally whenever she leaves the island. Presumably, she gets rejuvenated whenever she visits home.
In other versions, the immortality is linked to her status as an Amazon. When she is stripped of her powers (as happened during the mid 1970s) that probably includes the immortality as well.
If the author of Red Son decided that her powers were derived from an external source (Greek gods) then he might have decided that the unbreakability of the lasso and her youth were part of the package, and both could be taken away.