Lots of posts on this problem.
Believe me it isn't going to be easy to diagnose unless it happens quite frequently. I probably diagnose this problem 1-2 times a week.
The problems can include any of these pieces, Idle valve, idle switch or adjustment, decel switch, air flow meter (potentiometer) and even the speed sensor on the back of the speedo. Things like fuel pump relay are rarely the problem as that problem usually occurs on start-up or at any time. For it to shut the pump off just at idle would be a real coincidence.
The worse that can happen here is to jump from one tech to the next. Hopefully you have had someone that knows what he is doing but if the problem is intermittant and you don't want to play musical parts then stick with the guy who looked at it the first time. If not you will pay for basic testing over and over. Don't loose the preliminary testing that you have already paid for.
Owner 24 bay BSC
Bosch Master, ASE master L1
26 years MB technician