1. Mourinho's managerial philosophy - Mourinho has ONE way in which he manages (or atleast till date, has managed) all his clubs. Manage your team and buy fifa coins to upgrade your strength. He creates a siege mentality with an US vs THEM scenario in every club he goes to. With Porto, he was the underdog fighting against the big dogs, with Chelsea, it was the FA and referees and media being biased towards Manchester United, with Inter again it was the same, where he ticked off the media and other managers to get bad press and then generate this siege mentality.
Real Madrid, on the other hand, is a club with enormous prestige and honor. While the Barcelona hegemony was going on domestically, the Madrid faithful persisted with Mourinho's attempts at creating "this world is unfair mentality".
Once the hegemony was broken last year, the downswing in reputation of one of the greatest and most storied club in world football is beginning to test the patience of the faithful. Also, considering that Mourinho never stays at a club for more than a few years, this is obviously not the way forward for Real Madrid.
Dissenting voices are coming up. Another very important reason is the factions in the club. Mourinho's siege mentality is compromised by the close relations that Casillas, Alonso et al have with their Spanish teammates from Barcelona. And one thing you do not do at Madrid is tick off their legends who have been there for a decade and will be there long after Mourinho is gone, especially one who is called San Iker (Saint Iker) throughout Spain (not just Madrid)!
2. Mourinho's style of play - Mourinho employs a very high tempo, high pressing and fast counter attacking game at Madrid which puts insane amounts of pressure (workload-wise) on each and every player. This usually works with the siege mentality that he imparts (see above). However, this is problematic on two fronts.
Mourinho usually leaves after a short term leaving behind a group of players who are out of gas from the high intensity of play. This happened at Chelsea, this happened at Inter. I believe that the players are tanked out from last season, which was perhaps one of the most demanding seasons for every individual in that team. Also, every player was busy at Euro 2012, giving them almost no time for pre season recovery. Basically, they have been at this tempo for over a year and a half now.
The second reason why this is a problem is because the team is Real Madrid. Porto, Chelsea, and to some extent Inter can get away with this style of play, but for a Madridista, it is not acceptable. Real Madrid FC doesn't just win everytime, they win by playing the most beautiful football. This has been the Real Madrid way since forever. Again, while chasing Barcelona and while results kept coming, people put up with it, but now counter attacking against Celta de Vigo is not accpetable. Mourinho's system has to adapt (which he has tried to be fair, with Modric).
3. Form of key players - There can be no argument to the fact that the form of key players like Benzema, Di Maria and Higuain, and to some extent Ozil earlier, has failed to reach the glittering heights of last years campaign. They have flattered to deceive, though Ozil is finding form now. The defense has made numerous errors from crosses and set plays which is just unforgivable at any level of the game, leave aside Real Madrid FC. Is it a factor of being tanked out from last season, or just a dip in form, or a lack of sufficient practice in defending , this has played a huge impact. In the previous three seasons, whenever things were not going their way, Ronaldo used to drag them back by his sheer bloody minded brilliance, however he's been off color lately as well. Injuries to key players resulting in a not-stable back 4 has also been a huge factor, I guess, in the defensive lapses.
4. Other teams adapting to Madrid's style and Real not being able to adjust (highly related to the above points) - As mentioned above, Madrid are the bigger team and other teams will park the bus against them. Buy fifa 16 coins and build the best team to challenge players around the world. Madrid have not been able to sufficiently adjust and dispose of such teams. Against Barcelona and Atletico Madrid, the players raised their games in a more "open" match and played to their strengths. Against the lesser lights of La Liga and Spain, the fire seems to be missing. Again, may be a factor of the burn out from last season.