@JamesRobot Please see attached pictures.
If this A, it can be repaired, but this is really tricky (Heat VS rubber when you are soldering/repairing) Easier to just buy the rubber button.
If this B, if the black lclip from the connector is broken.
Yes you can solder it, but I don't recommend
Best option in my opinion, find a new connector and replace the old one. Those seems tricky to find, let me know if you need help. Maybe it is possible to buy the connector and only replace the black clip.
From what I understand, your situation is option B
For more pictures, please see