The Pokémon anime started regularly replacing Ash's travel companions once he entered the Hoenn region. First Misty was replaced by May and Max, then they were in turn replaced by Dawn once Ash went to the Sinnoh region. However, perhaps it didn't have to be this way.
There's a theoretical scenario where May stays on as Ash's travel companion going into the Diamond and Pearl series. She could have easily been the one to participate in Sinnoh's Contests instead of Dawn. However, perhaps there were more reasons why May needed to be replaced that need to be accounted for.
Why Was May Replaced In the Pokémon Anime?
It's important to keep in mind just why May was introduced in the first place. She initially replaced Misty so that Ash would have someone in his group who would participate in Pokémon Contests. Looking at things like this, Dawn wouldn't have to replace May because she shared the same passion.
Dawn was more likely brought in as a representative for Sinnoh and the Diamond and Pearl series as a whole. After all, she is the protagonist of the games the anime is named after, as well as Platinum. This is likely what the show writers were thinking when they had her replace May.
However, it's possible that May could have stayed regardless of her status as a Hoenn Coordinator. Ash has notably been the stand-in for just about every male protagonist in the franchise; this not only explains why they rarely appear but also why Ash's clothes sometimes resemble theirs. May might have similarly worked as a stand-in for Dawn and simply worn a similar outfit to her. She might have even caught a Piplup in Sinnoh.
The only problem with keeping May on the show was the relevance of Contests. Her goal of traveling with Ash to become a Top Coordinator was only relevant as long as Contests existed in the Pokémon games. However, Contests were removed from the games starting with Black and White. It would have been awkward for May to continue traveling with Ash unless she started entering Pokémon Musicals and Showcases. By that point, however, her career path would have to change from Coordinator to Performer. It's not impossible, it's just kind of odd.
In the end, replacing May might have been the best option in the long run. Her Japanese voice actress, KAORI, was diagnosed with spasmodic dysphonia as early as 2007. Out of respect for the voice actress, her role has been preserved, but she's been placed on an indefinite hiatus; this is why May hasn't had a speaking role since Diamond and Pearl. Even if May as a character could have theoretically continued to work in the anime, her voice actress couldn't have.
What Other Reasons Were There for Dawn to Replace May?
Besides all of this, there were a few more reasons to replace May. Keeping May around would also mean keeping Max around, which not as many people would be happy about. Additionally, Ash and Brock's Croagunk would be competing to keep him away from women. May and Dawn have a completely different set of rivals, none of whom are as interchangeable as the two of them. Similarly, the kinds of Pokémon they'd catch would be completely different; there's no guarantee that May would leave her Blaziken behind or catch a Piplup. Details like these seem minor, but they serve to differentiate Dawn from May and make her seem more worthwhile as a replacement.
As sad as it was to see May go, it was necessary. The anime had committed to the trend of replacing Ash's travel companions in each region and needed to commit to it. As far as replacements, go, Dawn made a pretty good one and some even prefer her over May.