I have a VW Golf 5 from 2004. I have bought it about 4 years a go. I have 2 pairs of keys. With the first one, I could never open the car remotely. The second one worked quite well but its range decreased over time. At the moment, I need to stand right next to the car doors in order to open them remotely. I tried replacing the batteries, that never helped. I would like to understand what is the case of such behaviour and fix those keys. This is the PCB from the car key:
If I understand correctly, the LED is only an indicator of the button presses and serves only for the user feedback. Please correct me if I am wrong. The U2741B chip on the 2nd picture is an RF transmitter. The big black rectangle next to it its the crystal osc. The M44C890 is the MCU. The top copper trace (looking at the pictures) is the antenna. The bottom copper trace is the positive terminal of the battery.
How can I investigate this? What could be the reason for range loss over time? I would appreciate all help.