I've read/seen a lot of interviews with Frank, and it generally sounds like he's done being a puppeteer. The fact that Sesame Street is the only franchise he occasionally moonlights on is telling, especially given that he himself is a father and, I believe, grandfather, and probably has a more sentimental attachment to the show and its characters (though a surprising percentage of his appearances have been voicing one-off Anythings, maybe done out of deference to Eric and David).
This is complete speculation, but I think he stays away because it's just a project he doesn't feel like he's a part of anymore, and doesn't have any more relation to SSW or the Muppets than a forty year old has to their high school (even if a few of his friends now teach there). When you watch old Bert and Ernie skits in particular, the raw chemistry between him and Jim is just so palpable, a lot of the jokes were made up by them in rehearsal and many props were obviously contrived last minute. For him to go in today and read lines he can't deviate from, to do some brief prologue for what usually ends up being a prerecorded musical number by Ernie...I can see how that would be depressing.
I'm a huge fan of Frank, and reading some of the stuff he says in, for instance, the Onion AV Club interview about his lack of sentimental attachment to puppetry, honestly does make me sad. But I don't think that bringing him back will have any miraculous impact, sad to say. Sesame Street today is still a good show, and The Muppets 2011 was a delightful movie but the spontaneous, bizarre magic of the old days isn't there. I don't doubt that somehow it can be approximated, but I don't think that more Frank Oz will accomplish this, at least not alone.