Your horse will start dropping his shoulder pretty much always in the same spot. You can use that knowledge to time your correction. Right before he starts speeding up and dropping his shoulder to head back to the gate, ride a very clean, somewhat abrupt transition to the walk.
Immediately start flexing him to the outside at a walk.
Keep that flex for a few steps, then do a hip-around to bring you back into the general direction your circle is going.
Then ride another flex till you get to the point where he usually stops trying to drop his shoulder.
Undoubtedly, your signals will have to be very authoritative. This is one of the spots where you and your horse hash out which one of you will be in the lead. Winning this battle will go along way towards building a better broke horse.
And since this will be in part a battle of the wills, do whatever you need to do to get it done. Wearing spurs is a good idea here. Get help from a trainer if you have to. Do Not loose the correctness of your aids, as you work on this. Click here if you aren't real sure what correct aids are.
The next step is to gain obedience at the trot.
At the same spot, ride a very correct, abrupt halt, then back up for several steps, and immediately out of the backup, flex to the outside for a few steps.
Right out of the flex, ask for a few steps trot, then ride another abrupt halt, back up and flex. That should get you to the spot where your horse balances by himself again.
And you can ride the rest of the circle at a trot.
As you build obedience, you will want to progress to the trot. As you work on this, you'll feel your horse become less set on dropping his shoulder. So eventually you can pass the regular spot and got into the corner of the circle.
But attempting to do a full circle at a trot, will only invite your horse to drop his shoulder again.
So ride him past the regular trouble spot and just a few steps afterwards, ride one of the halt-back-flex combinations.
Be vigilant for any sign of disobedience from your horse. If he even thinks about dropping his shoulder, ride the combination.
Be sure to bring him right back to the trot after each combination. Dropping the shoulder should not be an excuse for your horse to be allowed to walk. (They can be so sneaky...)
And last, but not least, we will try to stay at the trot. Ride a flex to the outside at the trot.
Only give as much leg aid as you need to, to keep the flexing. Not feeling your horse and what he is willing to give you, can result in him leaning on your leg. So be sure to ask and receive, ask and receive, pressure and release.
When you get good obedience at this point, you can start letting him have his own balance thru the circle. But as soon as he starts leaning to the inside again, you'll want to sharply flex him to the outside again.
Remember, this is a spot where you and your horse are wrestling for control. And you definitely want to be the winner in this match. Read this to find the correct balance in your partnership with your horse.