Why does the curtain rod get rusted?

Val, generally it's due to ever present moisture. Is your fan actually removing the moisture? If not, this rusty rod is likely your "canary in the mine" for a bigger problem. You may have a disconnected exhaust duct or a fan that needs to be replaced.

Humidity and lack of ventilation. Your fan may not be working properly. Do you leave the door open after showering? Is there a window you can crack open? Even a portable fan will help until you can determine if the exhaust fan is working properly.

We were using dehumidifiers in the bathroom, but it was only a masking technique. We finally put in a bigger exhaust fan and that took care of the issue

Hi, Val,

Have you taken off the fan cover and swept out all accumulated dust? If not, it adversely affects the fan's operation. Your fan should be sized for your bath, or slightly larger.

Newer models run very quietly and some have auto humidity sensors that come on when humidity is detected.

Be aware than fans should run during baths/showers, AND for a minimum of 30 minutes afterwards. Wipe excess water from walls and ceilings. Use towels and bath mats that never get laundered with fabric softener (reduces absorption).