It doesn't sound to me like he needs to repeat a grade. I would keep him where he is but get him a tutor twice a week. Begin tutoring now and continue it through the summer, perhaps cutting back to once a week. Tutoring can work wonders. Have him set an appointment with his teacher by email, phone or note, just like you would.
Teachers bend over backwards for kids, especially for a kid who'd take a significant step like that.
Please help with your thoughts on this issue. Some kids thrive on it and need nothing other than an intellectual challenge. If this is the case, perhaps adding more advanced classes to her regular program or a summer program would enrich her academic experiences without taxing her to the limits. Therefore, he is below grade level, the school says, in math. This really erodes his confidence.