About Rafa staying, personally, I'm glad.
He fucked up badly in the clásico (no Casemiro, seriously? Not only was that a tactical suicide, but it also seemed like he was scared of reading about him being defensive in a clásico on the following day's newspaper, which shows lack of character). However, the team has looked much more solid defensively throughout the season. Yes, the last 3 games have been shit, but the first 2 we had many injuries and this third one was a major fuckup by the manager.
I don't think it would be a good idea to sack him just because of this tactical mistake, no matter how much a 0-4 against Barça hurts.
If he keeps making mistakes or becomes unable to handle the situation then yes, sack him, but for now I think the club has done the right thing saying they believe in Rafa and strengthening his position. Sacking him now would just make it look like the players are in charge, and that's the last thing that should happen.