I’ve just had the same issue on a Hario Electric Buono kettle. I took it apart and realized that the bimetallic thermostat had rust on it, preventing it to do its work and “snap” when the steam reached it.
It’s a little disk made up of two different types of metals that changes shape with heat. In my case, the fix was easy: I used a metal brush to clean it up and it corrected the issue. It could be work taking a look at your kettle to see whether it could be the same issue.