Q. Suddenly, out of the blue, my car remote key stopped working. What could be the problem?
As long as the remote is not physically damaged, the reason is most likely to be low battery.
Car remote normally works on normal button cells. A couple of years after use, the car remote key battery dies out. Now, it is quite simple to replace the damaged cell. All you need to do is open the key, check the cell size / type and replace it with a new one. Button cells are available at any stationary or watch repair shop.
Just to be on the safer side, and to not damage any other tiny parts inside the remote key, learn it once from the authorized workshop as to how to open the key for changing the battery. Next time you can do it yourself without needing to take the car all the way to the garage!