This was a ReactJS component with state. Both handlers interacted with the state and updated it.
The fix turned to be quite easy but worth saving for later. The reason for that bug wasn’t immediately obvious, but it was the order of browser events. Blur comes before click, and any state change in ReactJs triggers a component re-rendering itself. So, onBlur handler caused the render() method to fire and that is why the second onClick handler was just lost.
The fix? Use onMouseDown in place of onClick.