To reproduce close the tab.

import javafx.application.Application;
import javafx.event.Event;
import javafx.event.EventHandler;
import javafx.scene.Scene;
import javafx.scene.control.Label;
import javafx.scene.control.Tab;
import javafx.scene.control.TabPane;
import javafx.scene.layout.HBox;
import javafx.stage.Stage;

public class TabPaneVetoTest extends Application {

    TabPane testedControl;

    @Override
    public void start(Stage stage) {

        initTestedControl();

        HBox root = new HBox(20d);
        root.getChildren().add(testedControl);

        Scene scene = new Scene(root, 300, 250);

        stage.setScene(scene);
        stage.setTitle(System.getProperty("java.runtime.version") + "; " + System.getProperty("javafx.runtime.version"));
        stage.show();
    }

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

    private void initTestedControl() {
        testedControl = new TabPane();
        Tab tab = new Tab("Vetoing tab");
        tab.setClosable(true);
        
        Label lbl = new Label("Content");
        lbl.addEventHandler(Tab.TAB_CLOSE_REQUEST_EVENT, new EventHandler<Event>() {
            @Override
            public void handle(Event t) {
                System.out.println("t = " + t);
                t.consume();
            }
        });

        tab.setContent(lbl);

        testedControl.getTabs().add(tab);
        testedControl.setMinSize(200.0, 100.0);
    }
}