To reproduce, compile and run

- open dropdown with mouse and select an item: this will remove the combo and re-add it to the parent
- click on re-added combo
- expected: dropdown opened
- actual: nothing happens

This seems to happen if the combo is removed while the dropdown is open. Indicators for that assumption:
a) select item by keyboard without opening -> behaves as expected
b) explicitly hide the combo before removal (in the listener) -> behaves as expected

Similar issue as JDK-8095306 which was fixed to handle the initial showing, but not the dynamic case. So the fix for this should be along those line, f.i. in skin's constructor, install a in a listener to the combo's scene property, which keeps combo's showing in sync with popup's showing

    registerChangeListener(combo.sceneProperty(), e -> {
        if (combo.getScene() == null) {
            // arguable:
            // on removal, the popup is hidden,
            // force combo to hide also
            combo.hide();
        } else if (combo.isShowing()) {
            // ensure popup is showing
            show();
        }
    });

Also, check DatePickerSkin and any other sub of ComboPopupControl if they have similar issues (initial and dynamic).

Code example (from SO https://stackoverflow.com/q/48538763/203657):

public class ComboBoxTest extends Application {

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

    @Override
    public void start(Stage stage) {
        VBox root = new VBox();

        final ComboBox<String> choices = new ComboBox<>();
        choices.getItems().add("Test1");
        choices.getItems().add("Test2");
        root.getChildren().add(choices);

        choices.getSelectionModel().selectedItemProperty().addListener(
            (observable, oldValue, newValue) -> {
                root.getChildren().clear();
                root.getChildren().add(choices);
        });

        Platform.setImplicitExit(true);
        stage.setScene(new Scene(root));
        stage.show();
    }
}