Actually I think Brian Henson does still perform, but pretty much only for The Jim Henson Company. I don't think he's physically performed any Muppet characters since the Disney purchase.
Bill Baretta was asked why Seymour was dropped during an interview at The Muppet Mindset, and he wasn't sure. I think he speculated that Brian Henson might not have liked the character but wasn't sure there.
I asked Jim Lewis about this in one of the "Ask Jim Lewis" threads. I don't recall him giving a speciffic reason, just saying that Pepe can work well on his own but Seymour needing somebody to work off. I'll have to find the exact statement.
A long time ago back in 2002 I sent an e-mail to The Jim Henson Company, asking about Seymour. I can't remember how I worded the question, but I think I asked why Seymour and Pepe stopped appearing as a team, and the reply I got was a quick "They broke up the act - That's show biz!" response. Too bad I couldn't get a real behind-the-scenes reason.
And of course there have been a few times when Pepe said what happened to Seymour (I believe the Muppet Wiki page for Seymour notes down both of these). At Muppetfest Pepe said that Seymour was living in a condo in Florida, while a few years ago on a talk show appearance Pepe said that his green card expired and had to move to india.
It's a shame that Seymour didn't appear in any of the Muppet comic books (or did he and I just don't know? Muppet Robin Hood is the only Muppet Classics comic that I've managed to find).