The landscape of action movies changed. Sometime in the 90s, respected dramatic actors started getting into the full-blown summer blockbuster action flicks. People still wanted to see big explosions and serious ass-kicking, but these actors (Cage, Snipes, etc.) could actually bring more to the role, even if it wasn't on the page.
The limited ranges of Van Damme and Seagal made them obsolete, especially since the good actors were getting all the good action roles. It even affected Stallone, though the way he picked one bad movie after another had more to do with it.
Now Schwarzenegger's range was about the same as Van Damme and Seagal, but he had massive on-screen appeal and his smart selection of roles made him one of the biggest movie stars in the world, even allowing for him to alternate between comedy blockbusters and action blockbusters.
But the changing landscape, which may have slowly began with Bruce Willis' "everyman" in Die Hard, meant that these action hero parts were doing more, you know, acting. And Arnold is larger than life (he didn't exactly look worn down and suicidal in End of Days no matter how hard he tried) when he's at his best (or at least most popular). I actually think he was pretty successful at playing an average joe in The Sixth Day, but look at the audience response to Junior -- people want to see him taking life, not creating it.
I think it was a combination of him not being talented enough to roll with the changes and the projects he took on simply not being as good as they used to be. Just ask Charlie Sheen what happens to all your cred (Platoon, Wall Street) when you put together a string of bad movies.