If your question was simply: Do you believe in Rafa?
I guess my answer is yes. I believe that Rafa has great skill in coaching, even though he is stubborn and not fit to run a transfer mercato. Rafa at his best can have his teams functioning on a level higher than anyone else. Examples are his Valencia sides and Liverpool at times last year. I think that like anyone else Rafa has become complacent. 5 years is a long time to go without the success you're used to and I believe Rafa needs to find himself in order to become motivated like he was at Valencia and during his early Liverpool years. That said I could easily see him going to Madrid at the end of the season to find a new challenge or motivation.
As for those who want to replace Rafa, I don't think this is something to be done over night. If you replace your coach you want to find someone better that can push the team to the next level. That can't just be anyone.
To conclude, I think Rafa has the skill and the available players to turn things around. It is a question of whether he has the motivation to do so. Can he get the players to rally behind him and play every match like its the end of the world? Can he admit that maybe he shouldn't have complete control over the transfer market? Can he make the tactical changes he did in his early years (at Pool) instead of insanely relying on a tactic that once worked a long time ago?
If the answer to any of these questions is no, I think he should leave. I don't think the club is going to fire him and I don't think enough fans will turn against him to force the owners to sack him. So it is up to Rafa and the players. I think in the end that Rafa's ability to keep confidence in the players will seal his fate.