The doyen of scriptwriting analysis, Syd Field, called the solution to saggy middle 'the pinch'. It was a scene which turned the story into a new direction. Terry Pratchett once suggested that all a writer had to do was bring on a naked woman brandishing a flaming sword (which would certainly send my novels into a completely new direction). Basically, something BIG needs to happen.
But when I say BIG the incident may, in itself, be quite a small action. It's the repercussions which are large. For example, half way through the film Gladiator Maximus is told that if he gets to Rome and wins the crowd over, he'll meet the emperor. Since he'd like to kill the emperor, this gives him the will to survive - and his desire for revenge drives the second half of the film.
Halfway through, Cinderella dances with the prince and they fall in love, without which none of the clock striking or shoe losing would be important. In many detective stories, it looks as if the mystery is solved when - da dah! half way through something happens that points the finger elsewhere (there's another murder which the No 1 suspect couldn't have done, possibly because the victim is the no 1 suspect).
I can remember laughing aloud when I read the mid-point event in Saint Maybe by Anne Tyler, it was so simple - just a line of dialogue, but it turned everything before up on its head by making the main character realise he'd been looking at life from the wrong angle. So, the solution for a saggy middle is an event which changes direction, and not 100 sit-ups.
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