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.

Most places use a wet batter for an onion:

Outback Steakhouse Bloomin Onion

4 Vidalia or Texas Sweet Onions

Batter:
1/3 Cup Cornstarch

1 1/2 Cup Flour
2 tsp. Garlic ?? minced 2 tsp. Paprika
1 tsp. Salt
1 tsp. Pepper
24 oz. Beer

Seasoned Flour:
2 Cup Flour

4 tsp. Paprika

2 tsp. Garlic powder 1/2 tsp. Pepper
1/4 tsp. Cayenne pepper

Mix cornstarch, flour, and seasonings until well blended. Add beer,
mix well. Cut about 3/4" off top of onion and peel. Cut into onion
12 to 16 vertical wedges, but do not cut through bottom root end. Remove about 1" of                petals from center of onion. Dip onion in seasoned flour and remove excess by shaking. Separate petals and dip in batter to coat thoroughly. Gently place in fryer basket and deep?fry at

375 to 400 1 1/2 minutes. Turn over, and fry an additional 1 1/2 minutes. Drain on paper towels.
Place onion upright in shallow bowl and remove center core with circular cutter or apple     corer. Serve hot with Creamy Chili Sauce.

Creamy Chili Sauce:
1 pint Mayonnaise

1 pint Sour cream

1/2 Cup Chili sauce
1/2 tsp. Cayenne pepper 

Try using Methylcellulose F50, it works very well to help a batter cling. You can see one way to do it using a pre-soak in this Fish & Chips Recipe - a 2% solution of F50 in water used as a dip before battering. I haven't tried it with onions, but I expect it would work well. Note that the methocel has to be well hydrated first.

Actually what I learned was after coating the onion with batter place the onion in the refrigerator for approximately 30 mins. Then take out and fry it. I tried it & it worked like a charm; the batter stuck very well

Fry the batter on a sausage to get the batter crispy, then slide the batter to the thing you want to put it on.

You can cook the onion in a pan before putting in the batter, after this, you can cook the thing as a whole for about 5-10 mins. If you fry the onion as a whole, it should keep together as a whole, if this is what you want.