The Risk of Failure is a two-fold element. In some ways, I might have divided it into two separate elements, but it seems easier (and more cohesive) to address them both at once, so here we go.
The Risk of Failure in this context is both the main character's fallibility (their ability to fail) and the consequences of that failure.
I think that a weak approach to either side of this element can undercut a story's impact, though it doesn't necessarily make it a "bad" story.
In The Wonderful Wizard of Oz and its MGM movie adaptation, the main character is facing a pretty serious obstacle. That is, she's stuck in a foreign land with no way to return home. If she doesn't find a way to go home, not only will she be trapped in a wonderful, magical place (which she is apparently not interested in at all) but her aunt and uncle will be forced to cope with the grief of losing their only [adopted] child.
While the stakes are realistic (not too big) and the obstacle is difficult, there is never any serious suggestion that she might possibly fail to achieve her goal.
Basically all she does throughout both book and movie is accept others, try to be fair, and cry when neither of those things work.
Seriously. She was denied the chance to see the Wizard for exactly as long as it took her to monologue why this was a Bad Thing and cry a bit, and this sorry excuse for a guard let her walk right in.
On the other hand, you might run into the problem of the consequences for failure being so catastrophic that your audience simply doesn't believe that the main character could fail - either because the story would be uninteresting after that point, or because the story would end after that because everyone was dead.
Did any of you really think that there was any way Goku would somehow fail to save the world and everyone in it this time?
So there has to be a decent balance between the stakes being high enough to be interesting, but the possibility of failing to reach the objective not ending the world (or the story).
Even George R. R. Martin, genius that he is, couldn't make his fanbase really believe that he would kill off Jon Snow. There was a huge chunk of his audience that, even with his horrendous reputation for killing all the characters you love best, simply refused to believe that Jon Snow would actually stay dead. His plot armor was simply too thick for that to be a believable possibility. (And GRRM might have been lynched for killing him permanently, so there was that, too.)
I think one of the best examples of believable stakes and risk of failure comes from one of my all-time favorite anime series: Fullmetal Alchemist.
Without spoiling too much about the ending, I can safely say that the consequences of failure were catastrophic enough that it would easily kill most of our favorite characters in the show. And while I spend every re-watch clinging to the knowledge that if the show ended like THAT then the followup movie would make no sense, there is a real sense of danger. The main characters fail at enough of their goals that this Big Goal doesn't have the plot armor that says it has to succeed no matter what.
Has there been a story (TV show, video game, movie, book) that you felt did this really well? Or a story that utterly failed at this? I look forward to seeing your thoughts!
Until next time, stay awesome, Inklings!