I wish I knew more about your GTI. I am making the assumption your car is not a turbo.
Is your engine surging or just powering off?
If the engine is surging check your Power Steering Pressure Sensor, if so, it might be messing with the ECU (Engine Control Unit). These sensors can corrode or get loose.
If the engine is just stalling, then it might be the Idle Air Control Valve (IAC), also called the ISC (Idle Speed Control) or AIS (Automatic Idle Speed). A problem IAC can stall the engine when you let go of the throttle. A good sign this might be the case is excessive RPM at idle. Make sure you check the hose to the IAC, and not just the unit.
Lastly, if your car is shaking when stalling, you may want to look into the TPS (Throttle Position Sensor). If it is, make sure you don't get a rebuilt one, get a new one for reliability.
These are just some ideas without knowing more. I'm no mechanic, just a tinkerer. So perhaps someone else has a better answer. Let me know, I hope this is at least somewhat helpful.