[Well I'll hold off on suggesting some things until you report back since he did well the other day.
But I will say that you should NOT MAKE him go past it. That's the worst thing you could do IMO. Say you are afraid of snakes. There is a snake on the sidewalk going outside your door and you want to leave. Would you want me pushing you toward the snake, the thing you are terrified of? Heck no. Same with horses. They get more emotional and unconfident when you force them toward something they are afraid of. He's NOT testing you, he's just acting out of instinct. Also since he is afraid food will not work. A horse wants safety, comfort, play, then food, usually in that order. He doesn't feel safe in the arena so he certainly isn't going to be concerned with food.]
One of my mares used to freak out every time we went down the woodland side of our riding ring. She was convinced that there were bears in there, even though she could see through the tall trees (no underbrush at all). She was also afraid of one corner at the arena where I used to go for lessons with her. She was also afraid...well you get the point. If I had never pushed her past any of the scarey places, I would have been able to ride in a straight line back and forth in front of my barn. If you know there is nothing immenently dangerous to your horse, then you have to push them past their fears otherwise the fears grow and take over and pretty soon you aren't doing anything with them. That is just my opinion.
As far as getting them past a scarey area, I find that as you are soon to come up to the scarey spot, you start keeping their mind focused on you. A little more gentle hand/mouth contact to remind her that you are there. Half halts, neck softening, bring her face to the vertical, and turning her face into the centre so she can't look directly at the area where she thought she saw something. You should look in to the centre too because you know how sensitive horses are to the position of your body and legs and she'll feel your focus. And push, push, push. I seem to recall that when Ambra would have her fits, she'd try to duck into the centre of the ring, and I would have to force her to do a small circle back onto the rail at that point and try again to get past it.
You can do it, you just have to be more persistent than your horse. And be quiet, and calm, but determined. If you feel like you are tired from trying for that day, then just matter of factly, ask your horse to do something that you know is no problem, where you know she'll be successful so that you can end on a good note. Then (in her mind) you haven't quit with her being the "winner".