Fine scratches on small brass pieces

A. Unfortunately, Steve, once you are to the "very high mirror finish" stage, the polish you use for that has almost no cutting power to remove those scratches. It's like trying to dig a foundation for a house with a teaspoon.

You need to go back to an abrasive that is about half as rough as those scratches. Rub in the perpendicular direction to the scratches until the original scratches are gone and the surface is covered with new finer scratches running in the direction you are polishing. Then you go to a finer grade, and polish at right angles to the new scratches. I don't know how deep the scratches are, and how many steps you'll need to go through, but the principal throughout is to polish perpendicularly to the previous step, not stopping until all scratches from the previous step are gone. Think about it for a few minutes and you'll understand clearly. Good luck.