How do I repair peeling outside wall?

Your best bet in my opinion will be to paint it then get a corner guard. Big DIY stores carry them. Some can be painted but I think the paint will chip off or wear off just like it does the wall. I'd get clear or if there is a corner guard that matches you wall color get that. They come as self adhesive and nail on. I've just been looking into them to protect our door frames from our dogs nails.

As stated above, a clear corner guard will fix your problem. I put one in my daughter's room, the self adhesive type, about 18 years ago. It made it through her and now it's the grand daughters' room, still looks great and isn't noticeable unless you look closely.

Agreed, they are worth the small expense.

I put them in a few places in a house we were in during the eighties where the corner paint always seemed to rub off. I repainted those corners, let them dry and put up the clear ones and never had the problem again. They were well worth the small expense we paid for them.

Try priming with a good quality exterior primer first and then paint again.