Audi A3 parking brake problem - what to do?

Check if the immobilizer light on the dashboard is flashing when the car shuts off. If it is, the immobilizer might be preventing the engine from staying on. Try using a different key if possible, or check if the key you have is damaged or has a low battery if it's a remote key. If the issue persists, you may need to have the immobilizer system checked by a professional. Let me know how it goes or if you have any further questions!