What does the secondary air injection (AIR) pump do? Haynes Repair Manual says, "The secondary air injection system is used to reduce tailpipe emissions on INITIAL ENGINE START-UP. .....The air injection pump is controlled by the PCM (engine computer) through the AIR relay." So, once the engine warms up, the AIR pump isn't used.
Chevrolet has put out a Service Bulletin # 04-06-04-015, dated March 2005, and a revised Service Bulletin #04-06-04-015A, dated December 2006. It states that you must replace the pump inlet tube, and position the tube between the battery and fender. Omitting this, might be the source of the repeats.
If the repairer replaced the air injection pump based solely on the trouble code, that may not have fixed the cause.