Possibly from the phrase neck and crop, in which crop may refer to the backside of a horse.
come a cropper (third-person singular simple present comes a cropper, present participle coming a cropper, simple past came a cropper, past participle come a cropper)
- (originally) To fall headlong from a horse.
- (Britain, idiomatic) To suffer some accident or misfortune; to fail.
- She came a cropper on the stairs and broke her leg.
1879, Anthony Trollope, chapter 67, in The Duke's Children:
I should feel certain that I should come a cropper, but still I'd try it. As you say, a fellow should try.
1922, Katherine Mansfield, At The Bay:
You couldn't help feeling he'd be caught out one day, and then what an almighty cropper he'd come!