Originally, GRRM said he'd merely been held back for Season 2, along with Edmure, Hoster and the Riverrun stuff (Riverrun being a fairly major set and location, so they wanted to defer the cost of building it to Season 2). Now HBO doesn't have him on their Tully family tree at all (whilst Edmure and Hoster are on there). However, if you think about it the Blackfish doesn't necessarily do a lot himself. He's there to be Robb's right-hand man, a job the Greatjon can do instead. They can also give his story arc in Book 4 to some steward, and then have Edmure take over his storyline at the end.

He's a prominent character but, at least so far, he hasn't done anything 100% essential that another character couldn't do instead.