They can be difficult to feed for some reason. Mine goes through stages. I just keep mixing the food i feed and they will eventually eat. I really cant say they love flakes, or pelletts or frozen. It seems they take better to clams if i do feed that.
How long has it been since they last accepted food ?
Were they eating before you introduced the new clown in the tank ?
I would follow the advice given by the other members above, but just also observe whether the Banggai's appear nervous as a result of the new addition to your tank.