First of all -- make sure she is not shod with too long of a toe or too low of an angle. If her angles are low, get her front feet stood up by setting the shoes back until the angle gets up to normal. I have had to set some up by putting front shoes back all the way to the white line and leaving the toe nails out completely. Rolling the toes will also help stumbling.
You might also check her for neurological problems. Have someone lead her and them pull her hind end over by her tail and see if she staggers or stumbles. Do it while walking and pull her both to the right or left.
If you get her feet set up correctly and she checks out OK, then, get this horse into the roughest terrain you can get into. Go through rocks, downed timber, up and down really steep hills and the like. The rougher the better. They almost all learn to pay attention.
I have had some that were just plain lazy and had tried everything else on. I got into them pretty good with a pair of spurs every time they tripped. They usually got a lot better pretty quickly.
If they still kept tripping, I considered them 'unsafe' and got rid of them. I've only had 3 or 4 of those in 50 years. One was an outside horse I was training for a banker in town. He was unsafe after trying everything -- BUT, he was a gorgeous golden palomino 3/4 Arabian. They kept riding him and he fell with their daughter and broke her arm and wrist in several places. She required several surgeries and her arm is still not right.