To answer you question, I use the local product available here, Sigolin.
After using, I handpolish with 100% cotton. No rinse, neither with or without soap.
The theory behind is, the cleaning product leaves a protective coating, slowing down the tarnishing process.
I would try this, no rinsing. And, search for agressive athmosphere where you store the item. Is there sulfur in the air? Smoking, or other smoke sources? Or do you have the item close to "agressive" food, like vegetables?
And to the administrator: No idea why the pictures are upside down, sorry...