Nah, Ash'll never leave. Even though there are many people who hate him, there are many more people who like him and would never watch the show without him.
He may have competed in 3 leagues, but there are hudreds of people out there in the anime world who are much older and have been trainer for much longer.
I don't think it matters that he loses to the first gyms in the region. Levels are rarely mentioned in the anime which makes sense. The first gyms in the games are only low level because it would be *slightly* stupid to have level 50 Pokemon right at the start of the game. In the anime trainers don't have to go to Brock/Roark whoever first, they don't have annoying people or weird plants that block their way. They could decide to go the Sunyshore gym first. They obviously make the last gym battle in the anime the hardest so it at least looks like Ash's team has got stronger. Yeah, so losing to the first gym isn't a bad thing.
Anyway, you have to remember that some trainers DON'T make it to the league. They aren't able to collect 8 badges in a year. I remember Oak saying the 2 other Pallet Town trainers were unable to make it to Indigo Plateau.
So my answer is...uh...yeah, Ash is quite strong. Not the strongest out there though, definatly. But that's to keep things interesting. Ash sweeping gyms and Elite Four members would get VERY boring. His Pokemon's strengths just seem to go up and down randomly sometimes though, to suit the writers needs...