I think the problem with some City fans is that you lot expect too much from one player in his first season in England.
Robinho is not the best player in the world, not even close but he's certainly very gifted and in the right setup with the right tactical approach and quality players around him can perform at the highest level. Problem is, many expect him to step up and make a difference every time things get tough and I'm afraid he is not a leader by nature, more like someone who can make a very good team even better, if used properly.
Plus, he knows he's the most valuable asset in the cub, virtually untouchable and they can't afford to press him too much about his inconsistent performances or off the pitch behavior, those Brazilians are notoriously moody individuals and require a certain approach from the management.
It'll be interesting to see what'll happen with him in the summer if City fail to land any big players. That may prove to be his biggest test yet to see if Robinho is serious about sticking with City or starts angling for move away. Given his past behaviour at Santos and Real he doesn't appear to be a loyal type, but people do change and mature with time so only time will tell.