Removing blotchiness on sterling surface that will not polish out

[Ag999]

I usually have no trouble polishing badly tarnished silver using a good quality non-abrasive polish. But occasionally I get a piece of sterling with some type of blotchiness on the surface that will not polish out. It is not a coating of anything. I have never been able to find out what causes that blotchiness, but more importantly I would like to know how to safely remove it or polish it out. As you can see from my photos, it is more apparent in some lighting than in others.
Any advice you can provide would be much appreciated.