2003 Passat Seconday Air Pump

My check engine light came on. I was a thousand miles from home. The diagnostic code said it was the secondary air pump. A new one was put on. I drove a thousand miles back to New England and the check engine light came on again. My mechanic here said it was the secondary air pump. He looked at the pump, asked if I had the one they took off which I didn’t. He said the pump looked fine, reset the system and the next day the light came on again. He said it was probably just a small leak and to continue driving the car. Now about 6000 miles later I’m beginning to wonder what affect if any this is having on the car. I don’t notice any change in the way it drives. Any suggestions?

Denns