The secondary airflow system exists to heat up the catalytic converters under cold start conditions so they start working faster. The system only activates when the engine is started when cold. As you noted, the pump runs for about 30 seconds and doesn't come on again until the car is cold started again. Based on how my E46 operates, I think "cold" is defined by a certain ambient temperature, so the system may not even operate at all if the ambient temperatures are above a certain level.
On the 745, the pump runs and the air pressure of the pump causes the valves to open up. Air from the pump then flows through the valves, into the exhaust manifolds and on into the catalytic converters where the extra air causes the extra fuel in the system to burn which in turn heats up the converters. The extra air flowing in the exhaust mainfolds is sensed by the o2 sensors. If the sensors don't see a lean condition from the extra air, codes get set in the computer for improper secondary air flow. Your passenger side O2 sensors aren't seeing the lean condition, so the low flow code is getting set.
The sad thing is the car will work perfectly fine without the secondary air system. The cat converters would just take a little longer to heat up.....
If you have replaced the offending valve and hose, and you have confirmed that the pump is working properly, then it is likely that the Air Intake Tube that goes between the valve and exhaust manifold (#9 or #10 from the picture below) is clogged with carbon. If you have DIS, you can activate the pump to test it and run step by step diagnostics on the secondary airflow system.
If you can get a piece of the right size hose and connect it to the input of the valve, you should be able to blow into it and see if it opens. If it is working properly, you should be able to blow air freely through the valve. Try both sides and see if one works and one doesn't.
If you find one passes air and one doesn't, the Air Intake Tube is probably clogged. I would remove the valve on the clogged side and then start the car to see if any exhaust comes out of the air intake tube. If one of the tubes is clogged, you will probably have to remove it to see if you can clear the clog. Its possible that a passage in the exhaust manifold is clogged too.
I suppose its also possible that the intake tube to the air pump is blocked or partially blocked too, so make sure and check that too.
Last edited by joej85; 06-03-2011 at 12:20 PM.