John J-
It should clean up and then stay bright if you use a regular stainless polish like those used on copper and stainless pots or specific ones intended for marine use.
Are you using steel wood? Using ordinary steel wool causes problems. The steel wool is not stainless, and rubbing a stainless object like the sink or railings or other hardware causes the non-stainless wool and the stainless fittings to weld together on the microscopic level, then break those welds, with some of the non-stainless steel left on the surface of the fitting(s). This steel then goes ahead and rusts. You get the same effect using a wire brush or wire brush wheel that's not stainless. (I learned this from a metallurgical engineer from Westinghouse's Marine Division.)
If you need to use a more aggressive abrasive than ordinary polish on a stainless fitting, use very fine wet/dry emery paper to start with, or go to a marine store where you can get stainless steel wool. Also, there are more aggressive polishing compounds available if you can find them. Joe.