Though it wasn't actually on the show, there was once that Ernie left for a little bit, in the book Ernie's Big Mess. It's been years since I actually read it, but I know he'd made a mess of their place, and Bert got mad and stormed out. Ernie packed and left while he was gone, I know he at least went and stayed at Big Bird's nest but found the sticks too hard. I think he also tried to go to Oscar's can but Oscar told him to scram, and I'm thinking there was one other place he went. Eventually Bert found him and told him to come home.