"Put on a brave face" is to express that someone try to hide it's feeling and pretend to be alright. What if someone tries but fails, can I say, "He lost his brave face after that"? Or what would be a better word or phrase to express this situation?
Well, that depends on a few different factors, such as
You haven't supplied too many details about the scenario, so there is room for some interpretation. I'm assuming that this person wasn't very brave to begin with (based on how you said this person will "try to hide feelings and pretend to be alright"), and that maybe everyone else thinks that some humility came with the failure (otherwise, you might have inquired about "I lost my brave face" instead of, "He lost his brave face").
So, I'm assuming that that this person is thinking pretty highly of himself when he puts on his "brave face," but you want to describe his feelings afterwards, when that bravado is proven to be hollow. So long as those aren't inaccurate assumptions, here are a few idioms you might consider:
Most of these idioms focus more on the humility that accompanied this person's failure when they "lost their brave face." If you'd rather focus on how the person became less confident instead, you could simply say, "He lost his courage."
I agree with Bill Franke that a form like “He put on a brave face, but he lost it when he got scared” is acceptable; but “he lost his brave face when he got scared” is less acceptable for several reasons. Perhaps the most important is that because it isn't idiomatic, people may interpret it literally, and may envision the person actually losing his face, as opposed to merely changing expression from brave to frightened.
Among many words pertaining to a change from brave to scared or up to down are