Why does the idle bottom out when it drops from high RPM?

[MK3_Turb0]

My engine cuts out whenever the engine RPM drops from over 2000+ RPM. For instance, whenever I pull the car out of gear at a light or to downshift around a corner, as the RPM drops, the engine stalls out.

It is frustrating restarting the car every few minutes and can be dangerous on turns when the power steering goes out.

Is this a vacuum issue?
The car is heavily modified and has an AEM ECU, though I don't think it is related to the ECU. It's been in the shop a couple times, but they can't seem to find the issue. YOUR HELP IS GREATLY APPRECIATED! THANKS!

[S-mk3-B]

That ECU could probably be the issue or related in some way, as well as the mods since you said it was "heavily modded". But first things first, are there any error codes that come up? And does this problem happen when you rev in neutral as well?

[cre]

If the car has a BOV instead of the factory bypass setup (aka BPV) then that may be the problem by itself. The AEM can be tuned to account for this. This is only a possible issue if you're running the stock KVAFM or a MAF. Speed/density (MAP) setups are generally not susceptible. There's not a lot of help which can be offered if the car is heavily modded unless you begin posting exhaustive details about the build, ECU tune, diagnostic and runtime logs and so on.