The Plasticity of Blind Faith
The first challenge to blind faith comes with the acute realization that blind faith is aimless... you can believe in anything you want, you can take anything on faith, any scripture, any prophet, any ideology. Belief is plastic. If you have to believe, why restrict yourself to what you are being told? Make your own beliefs, be heretics. People don't do so, because they share the beliefs with a community, and there is an unconscious pressure of conformity. However, the realization of the plasticity of pure belief is a potential step towards its dissolution.
Apart from dissolution, there are two ways in which people respond to this. One is that they begin to say that their faith is not blind but rather based on reasoning. The off-side of this for the believer is that bad reasoning can actually be analysed and pointed out. To avoid this, the believer of 'rational faith' usually keeps switching from reasoning to faith during argumentation as and when it suits the purpose, and yet remains in denial about faith being essentially blind.
The second reaction to plasticity is to resist it strongly and become a fundamentalist. You over-react and adhere so intensely to a limited set of beliefs that you begin to see followers of other variants of your own faith as heretics and apostates.
[Edit: After reading F's comment. I realized I had over-looked another possibility, the one of living with faith while at the same time recognizing its plasticity. This position allows for greater tolerance.]