little and often with repitition. Also have regular breaks. Do all the obvious things like making sure you work for equal time and intensity. Also get the horses back, teeth and saddle checked. It may be one sided due to a physical problem.
I have the same problem with Argo. You need to work her longer on that rein, try turning tight circles and pushing her back out keeping the bend. Also lunge her for a bit longer on that side. It's so frustrating isn't it!
When hacking out try to get her to strike off on the weaker canter lead too...let me know if you have any other ideas!
When you're working on the stronger side, try bending slightly to the weak side, i.e. if you're on the right rein and it's your good rein, then have some outside bend to the left, so you're working the weaker side more often.
The other thing is to concentrate on your position - make sure your aids are equal and you're sitting straight on both reins. My horse is weak on the left rein, and I'm also crooked to the left, so we're a bit stuck in catch-22 situation at the moment.
You could try other lateral work such as shoulders-in. With your horse falling out, then I'd try leg yielding in away from the fence.