Hyundai Repair: 2006 Tucson Engine cuts out, air flow sensor, throttle position sensor

Question
I bought a 2006 Tucson in Feb. of this year and recently I've found that my engine will unpredictably, and without much warning just cut out.  I brought it to the dealer who ran the computer diagnostics and replaced the brake switch and another sensor, that was more related to my ESC light randomly turning on.  I brought the car home, and I am still having random engine "give outs."  Typically they happen on deceleration, after going over a speed bump, or after a succession of tighter turns followed by decelraton (ie, parking lot driving)  I have a feeling there may be a short in the system that the computer can't detect.  I'm brining the car back this week for them to try to look for the problem again, but they say that since they can't duplicate it, it's going to be difficult.  What do you think?  

Answer
It seems to be primarily an issue with maintaining idle.  If I were diagnosing, I'd want to check for any engine or transmission diagnostic trouble codes, and if there are any possibly related codes present, start with diagnosing those.  I'd also be very interested in checking the air flow sensor, the throttle position sensor, and the idle actuator, and checking for vacuum leaks and proper attachment of the air intake bellows to the air flow sensor.

But if all these things provide no hints as to the cause, and the condition won't occur for the repair facility, they're correct that it'll be difficult to figure out the problem.