Audi,How do you know if your secondary air injection system is bad?

I have a check engine light on that the code states that I have a vacuum leak to my secondary air injection system. I replaced the vacuum hoses and reset the codes and the car drove over 1500 miles before the engine light came back on with same code. I replaced the vacuum hoses with new ones and the connections seems to fit properly how to i tell that the secondary air injection pump is actual bad?

Thanks,

David A.
My car has a manual transmission.