This happens if the editable property is dynamically set to true after the skin is created. The example below compares a combo which is editable from start with a combo that has its editable set via a button.

Run and
- open the popup of the initially editable combo
- click on the arrow: popup is hidden - expected behavior
- click on the button to make the other combo editable
- open popup of other clickup and click on its arrow
- expected: same as first combo, that is hide popup
- actual: popup hidden and shown again

Technical reason is ComboBoxBaseSkin: it registers the mouse handler only if the combo is editable at that time of skin instantiation. Aside: fixing this will make a complete hack around JDK-8150951 even more hacky ;-)

public class ComboEditableArrowHandler extends Application {

    private Parent getContent() {
        ComboBox box = new ComboBox(FXCollections.observableArrayList("one", "two", "three"));
        box.setEditable(true);
        box.setValue("initial editable");
        ComboBox core = new ComboBox(FXCollections.observableArrayList("one", "two", "three"));
        core.setValue("dynamic editable");
        Button toggle = new Button("toggle editable");
        toggle.setOnAction(e -> {
            core.setEditable(!core.isEditable());
        });
        
        return new VBox(10, box, core, toggle);
    }
    
    @Override
    public void start(Stage primaryStage) throws Exception {
        primaryStage.setScene(new Scene(getContent()));
        primaryStage.show();
    }

    public static void main(String[] args) {
        launch(args);
    }
}