Answer: Bad cut, low clarity, or fake diamond.
Step-by-step explanation:
Poor cut would be number one. It affects how light bounces off and passes through the stone. Second would be poor clarity (when it has imperfections inside which block/diffuse/affect the way light passes through the diamond). Lots of tiny scratches and nicks on the surface would also affect brilliance, especially if the diamond is on an old piece of jewelry, which was rarely taken off by the previous owner regardless of what kind of work they were doing.