A diagnostic system for a vehicle is disclosed. A first difference module generates a first difference based on a first pressure measured at a first secondary air injection (SAI) valve and a previous value of the first pressure. A first summer module generates a first accumulated difference based on a sum of values of the first difference generated during a predetermined period. A second difference module generates a second difference based on a second pressure measured at a second SAI valve and a previous value of the second pressure. A second summer module generates a second accumulated difference based on a sum of values of the second difference generated during the predetermined period. A fault indication module selectively indicates that a fault is present downstream of one of the first and second SAI valves based on the first and second accumulated differences.