I wouldn't be surprised if Robson's days are numbered and that it won't be long before he's replaced by either Lyth or Lees of Yorks. certainly for the forthcoming tour of the Caribbean.
England are slow to discard players these days, unless you're a fast bowler. 1 x 100 and 1 x 50 in his first 9 innings is enough to keep him in the team for this series. He will have to bat very poorly in the last two Tests to jeopardise his position. But even if he does, and England win the series, I'd expect him to remain - they do like to keep a winning team together.
The WI tour is 8 months away, but before then we have a plethora of ODIs, so Robson can sit back and watch his rivals make a mess of things.