Faith is a difficult word to use sometimes because many people can't think of the word 'faith' without also thinking of the word 'irrationsl'!
I don't think that making a BP is an irrational leap of faith. It's a rational thing to do. But it's not purely rational because the decision cannot be fully confirmed by your prior knowledge and experience. It's a new and deeply changing experience and one that you haven't gone through before.
Even if you find yourself making a BP more than once, each time you make it is still a new experience because you've had to analyse why you failed and account for this in your new decision.