Answer

By Your Horse

Show jumping trainer Carol Mailer says…

Horses run out because they can. I don’t think you’re doing much wrong, as you’re very sensibly reschooling your horse and working over trotting poles, etc.
You must give your horse no option to run out and be far more insistent he stays straight. Having someone standing in the way is a disaster: what if your horse knocks them over?
Are you trotting to the fence? Your steering should be much easier the slower you go. If your horse is doing trotting poles nicely, add a jump at the end of the line and stay in trot.
Maybe this willingness to go forward is an evasion in itself to avoid staying straight. You mention your horse is going from your leg, but is he escaping through your hand?
Ask yourself whether you’re giving your rein away when you reach the take off point. If so, don’t give the rein to the fence and instead hang onto your contact all the way.
Build a grid against the arena fence so your horse can’t run out. If you haven’t got a fence to work along, take him somewhere that has.
Always position your horse to the middle of the jump, using a cross-pole. If he goes where you point him, it will be easier when you change rein or no longer have a fence to help you.
If you insist your horse faces the middle of the jump and he decides to stop, don’t worry. As long as your steering’s OK, he’ll realise he has no other options but to stay straight and jump. Remember, be methodical in your approach, don’t over-face your horse and go slowly.