TTT is correct, chrome does not rust; it's the steel underneath which rusts when the chromium plating gets perforated or scratched. The only solution is to buy a better quality mirror which will have thicker chromium plating or have a layer of, say, copper between the steel and the chromium. Once the rust starts you'll never really prevent it from keep coming back. Perhaps you're too young to remember the chrome-plated bumpers on 1960's cars which were prone to rust, except for Rolls-Royce who copper plated the steel before chromium plating it.