The Pokémon anime has been going for nearly 25 years and a lot has happened. Ash Ketchum and his partner Pikachu have met all sorts of people and Pokémon on their countless adventures. Despite all of these experiences, however, they never show any physical signs of aging.
There are many theories about why Ash and Pikachu don't age. One theory suggests it's because the Ho-Oh that Ash and Pikachu see in the first episode granted them eternal happiness in the form of endless adventures. A darker theory suggests that Ash has been in a delusional coma since that same episode. A darker theory, still states that Ash has been dead the entire time. This last theory is a little too dark by the Pokémon anime's standards, but there is a logic to the idea that makes it worth considering.
The theory stems from Episode 23 of the anime, "The Tower of Terror." The episode features Ash and Pikachu looking for Ghost-type Pokémon to use against Sabrina's Psychic-type Pokémon. Their search brings them to the eponymous Pokémon Tower, a Pokémon burial ground in the games that the anime remodels into something of a haunted house. While in the Tower, a chandelier falls on Ash and Pikachu and knocks them out. A Haunter takes this opportunity to pull Ash and Pikachu's souls from their bodies and have some fun with them. The implications of Ash and Pikachu shedding their mortal coils is the basis for the "Ash is dead" Theory.
One Redditor, in particular, expands upon this theory in a unique way. u/askthetyrant2 suggests that if Ash were an ordinary human, the Ghosts-type Pokémon would not interact with him the way they do. They should simply scare Ash, get their laughs in and disappear into the night. They give Team Rocket this precise treatment.
However, when Ash interacts with them, they do a little more than play pranks on him and his Pokémon. They battle him, perform manzai, a traditional style of Japanese comedy, for him and even invite his and Pikachu's spirits to their secret playroom. It's possible that the ghosts give Ash and Pikachu this special treatment because they recognize them as fellow specters.
askthetyrant2 goes on to suggest that Ash's other interactions with ghosts and Ghost-type Pokémon may also have to do with his loose attachment to the realm of the living. They offer the episode "The Ghost of Maiden's Peak" as an example and asks for those commenting to suggest other encounters. Ash is possibly able to see other ghosts clearly because he himself is a ghost.
If the theory holds true, it would explain a number of things. The reason Ash constantly starts his journey over from scratch in new regions is that he regrets never accomplishing his dreams before dying and cannot move on. The reason Pokémon battles don't work as they do in the games is that the undead 10-year-old is using his limited understanding of battles to craft them in his mind. Ash's friends and family don't age either because he can only see them as he knew them in life. Any new adventures he has or new friends he makes are all part of his time spent in Heaven doing what he loves best. These are just a few of the things that can be explained if Ash and Pikachu are on permanent vacation, but there are far more out there.
Of course, all of this is only speculation on the part of the fans. If anyone on the Pokémon anime staff were asked about this, they'd likely just clarify that Ash is alive. Killing him off would be much too dark for a kids' show. The simpler answer for why Ash never ages is because it's an anime and the writers want to keep Ash 10 years old to best mirror their target audience. But it's still fun to think about the logic behind Ash's everlasting youth as it leads to interesting (and creepy) ideas like Ash and Pikachu being dead.