Incurable BMW Idle Issue - 2 bmw repair garage stumped..help!

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I have a 2001 BMW 330I with 218,000 miles on it. When I am driving it and am slowing down and take it out of gear sometimes the car dips down to 400 or 500 rpm and the car shudders (not all the time but often) and then bounces back up to 700 or so where the idle should be. I’ve had the throttle sensor and throttle body ( I think??) replaced. I also had the CATs replaced recently due to the sensor saying they were basically plugged, which I thought might be the problem with the throttle, but didn’t cure it. If someone could give me some insight I would be grateful. I love this car but this issue is driving me nuts. Thanks much!

On some cars, a relearn procedure must be performed when a throttle body is replaced

Where have you been taking this car for repairs and service?

Can you hear any obvious vacuum leaks?

I will assume you still have that cat low efficiency code, correct?

Any other codes?

Some e46s do have a tendency to plug up catalytic converters, but there is no computer code that indicates that. The catalyst low efficiency code almost always means that the oxygen sensors are getting old and slow. I presume that you got new oxygen sensors when you got new cats, so whether the cats were plugged or not, that problem is fixed now.

Like db4690, my suspect is vacuum leak or air path leak. When the car first goes down to idle, the mix is mechanically way off, and it takes a second for the computer to compensate.

If it were an air path leak, they would have seen it when they were replacing the throttle body, so that rules that out. Next candidate would be intake manifold gasket or crack in intake manifold. Try spraying diesel starting fluid (ether) around the intake manifold and see if it impacts the idle.

Another thought - Is the problem affected by whether or not the air conditioner is turned on?

It does it as well with the A/C on and or off but I will see if it gets better with the A/C turned off. Yes, the O2 sensors were replaced. I will also check into the relearn procedure. Thanks much for the help!