There was little in the way of actually disproving Ash aging until the English dub went and outright said he was 10 at the beginning BW. Now, I'm not sure if this even happen in the original Japanese dialogue, and if it didn't, there's really no other evidence to support the notion that Ash has remained ageless throughout the entirety of the anime. In fact, as early as the first season, the English dub acknowledges that Ash has been traversing through Kanto for an entire year so.... the conclusion I arrive at is that the English intepretation is all over the place, and we shouldn't let one line at the beginning of a "reboot" season stand in the way of assuming that Ash has indeed matured in some form over time.
I mean really, there's SO many things that point towards Ash maturing, both in stature and in development as a Pokemon trainer, up until the beginning of BW. Not only did we have the aforementioned Narrator quote about the passage of time, we also see Ash gradually getting better as a trainer. If every single series opened as BW did, with Ash being a complete idiot and acting like he'd never had a battle in his life, I'd understand that they writers/creators mean for Ash to literally "reset" each series, and that his age would remain unchanged. But we see as early as the Johto series that Ash is getting progressively better as a trainer, despite him using new Pokemon every generation. He gradually finished in League tournaments higher and higher, which even climaxes at the end of DP with him being in semi-finals against the single most powerful trainer we've seen in the anime thus far, Tobias (to those curious, it's stated that Tobias swept every single gym in Sinnoh with his lone Darkrai, with no one else having a clue what other Pokemon he possesses). Ash even DEFEATS Tobias' Darkrai, only to be bested against his Latios, something not even a single Sinnoh Gym Leader, or even a competitor in the Sinnoh League Conference, could do. We also see Ash go from being mentored in Kanto by Brock and Misty, to being the mentor in Hoenn and Sinnoh to May and Dawn respectively.
If that wasn't enough, we also have his actual design and voice to work with. You can chalk it up to the chance in voice actors all you want, but Ash clearly has a somewhat deeper voice from Battle Frontier on, which may or may not be on purpose, but I'm inclined to believe the former. The OP also points out his design change over the years, which I believe also indicates an older protagonist.
The one thing that stands in the way of this is how Ash behaves in BW, coupled with that Narrator quote that says he's 10. I honestly think BW was going to be a "reboot", as it was a perfect opportunity because Black and White the games featured an entirely new cast of Pokemon. Ash was hit with the stupid-beam, and thus years upon years of character development and knowledge were lost. I've admittedly haven't watched a single episode of the XY anime, something I might change in the future, so I would like to know if Ash has actually picked up where he left off in DP, if it's more of a continuation of BW, or if it's just like a "reboot" again in some ways.