I know Brightpowder is sometimes banned. Also, why is it sometimes banned?
I assume this is a Metagame question, but I'm probably misinformed. xD
Brightpowder and Soul Dew are banned from the current OU/Uber Metagame, as far as I know, and just Brightpowder for NU/UU.
For Little Cup, only Berry Juice and Deepseatooth are banned.
Also remember that some trainers enforce the "Item Clause," meaning no two Pokemon can have the same item.
If I'm not mistaken, it's passivelly reduce opponent accuracy, right? (maybe) It's banned like the other reducing item. I think item which not banned are "plate item", like fist plate and earth plate, and "HP restored item", like leftovers and shell bell, and item that increase power, like charcoal and poison barb! (i think...)