My next best guess, based on what you've told me, is that he's a very smart boy, who is capable of doing high-level work during the short-term, intensive, and challenging testing, but he's bored to tears in school! Do you and his teachers think that he's being appropriately challenged, or are they still trying to feed him the stuff he has really known for long time? What about letting him jump up to something more challenging? What about having him tutor younger kids (or same-age kids from another school)? What about letting him take a ninth-grade class, or part of it, to see what he's made of intellectually, to give his ego a boost, and to let him hang out with some really cool, big kids? (Careful here.) Or enroll him in an enrichment program at the local museum. (Here's a radical suggestion: Have him do that instead of some grade-level boring stuff and let him earn a grade for it.) Anybody worried that the other kids will be jealous? That will just mean your son has more status, which should make him feel better.
Here's my last hunch -- and I hope it's not the case -- but perhaps your son is upset by something or even depressed. You didn't say anything about his social skills or whether he's a happy kid. He may spend so much time worrying that he doesn't have time to think about or do his school work, even though he's capable of doing the work. Check this out by having a psychologist interview him and give you his impression. Let us know if any of these hunches are on target.