Some batter falls off during deep fry
From Alton Brown's I'm Just Here for the Food (p. 99): "The number one reason breadings fail (fall off) is too much primer coat (flour). There is nothing to hold the layers together so they unzip from each other and your breading is floating free in the fryer..."

If you're going to use a three-stage breading process, which is what you've described, you need to make sure to shake off as much of the initial flour layer as possible.  Dry flour doesn't stick to itself very well, so if a too-thick initial dredging creates clump-like layers of flour that aren't well moistened, in the relative violence of the fryer the dry interior of those clump-like layers will separate from each other and your breading will flake off.

For "bloomin' onions," the process I've seen wasn't a three-stage one like you describe.  Rather, the onions were stored/soaked in milk (because soaking in a slightly acidic liquid mellows the onions -- water should be as effective, and soaking may not be necessary at all), and, as needed, pulled out, shaken free of excess liquid, and generously dredged in seasoned flour.