Going back 50+ years to school chemistry, we were taught that it was electrolytic action between the chromium and the steel which caused the steel to rust. You can clean it off but it will come back. In the days of cars having chromium-plated bumpers the likes of Rolls Royce copper plated the steel and then chromium plated the copper; separating the steel and chromium with copper caused the copper to degrade instead of the chromium (I think).
The bottom line is that once the rust has started to appear you can't stop it, just keep cleaning it off. Chrome cleaner, you can still probably buy it from car-accessory shops, will clean the chrome nicely but not cure the problem.