Moisture is the cause of rust and such paint peeling, so if you do not have a leak, water has to be coming from somewhere.
Dampness will cause this sort of damage, and have seen it on ironers,appliances, and other painted metal objects located in damp/humid conditions. This is probably one reason many like stainless steel for surfaces instead.
You can stop the problem from getting worse, by scraping or otherwise removing all loose paint and rust, applying a "Restoleum" type product, then applying a coat or two of applinace paint.
Sooner or later you should address the dampness, otherwise the problem will likely occur again.
L.