Since the problem I had is mentioned numerous time on this forum and always remained without a solution, I went for a simple yet hacky approach to solve it and keep the OEM system in place.
We know that the parking aid would come to life after either disconnecting the white plug on the PDC ECU or clicking save in TOAF with the ignition on. It seems that the system needs some kind of re-registration of the sensors every time the ignition is turned on. If something can be triggered manually, it can also be done automatically.
All the wires on the white connector come from the sensors. There is a brown one for each sensor. Those are the positive 12 volt wires. I cut these close to the connector and bundeled all 4 wires (on the side coming from the sensors) together and connected those to the green/brown wire for the reverse light. By doing this, the sensors are powered only when the car is put in reverse instead of being powered all the time as soon as the ignition is turned on. This will re-register the sensors every time necessary and keep the system functioning, even after turning the ignition off/on.
Should there be any problem, fuse 41 for the reverse light and cruise control will blow, but for me this has been working perfectly.
This is a picture of how it works before tidying the harnesses up:
