Maybe you are unconciously throwing him off balance. Pay attention to see if you are leaning into the turn. You need to stay in the center of the horse.
Also, make sure your saddle fits him. The placement of the saddle is critical, and if it's too far forward it's going to block his shoulders, thus making it hard for him to turn. Find the edge of his scapula (shoulder) while at rest. Mark it with a piece of chalk. Then, while someone else holds him, pull his leg up and out in front (so you are holding his leg next to your hip) and slowly run your fingers along his scapula until you feel it "drop off" like the edge of a cliff. Mark that spot. This is where his maximum range of motion is with his scapula, and the first weight-bearing part of your saddle needs to go directly behind this spot to fully free up his shoulder.
You will notice that your saddle will dip down in front, making it down hill and putting pressure on his withers and shoulders. This is where shimming comes into play. You'll need to shim your saddle so that it's even. Feel free to PM me for further details on that.