Java - how do I prevent WindowClosing from actually closing the window

This is the key, methinks: frame.setDefaultCloseOperation(WindowConstants.DO_NOTHING_ON_CLOSE); Makes the difference in the test case I cooked up.

not sure where is your problem,

import javax.swing.*;
import java.awt.*;
import java.awt.event.*;

public class ClosingFrame extends JFrame {

    private JMenuBar MenuBar = new JMenuBar();
    private JFrame frame = new JFrame();
    private static final long serialVersionUID = 1L;
    private JMenu File = new JMenu("File");
    private JMenuItem Exit = new JMenuItem("Exit");

    public ClosingFrame() {
        File.add(Exit);
        MenuBar.add(File);
        Exit.addActionListener(new ExitListener());
        WindowListener exitListener = new WindowAdapter() {

            @Override
            public void windowClosing(WindowEvent e) {
                int confirm = JOptionPane.showOptionDialog(frame,
                        "Are You Sure to Close this Application?",
                        "Exit Confirmation", JOptionPane.YES_NO_OPTION,
                        JOptionPane.QUESTION_MESSAGE, null, null, null);
                if (confirm == JOptionPane.YES_OPTION) {
                    System.exit(1);
                }
            }
        };
        frame.addWindowListener(exitListener);
        frame.setDefaultCloseOperation(EXIT_ON_CLOSE);
        frame.setJMenuBar(MenuBar);
        frame.setPreferredSize(new Dimension(400, 300));
        frame.setLocation(100, 100);
        frame.pack();
        frame.setVisible(true);
    }

    private class ExitListener implements ActionListener {

        @Override
        public void actionPerformed(ActionEvent e) {
            int confirm = JOptionPane.showOptionDialog(frame,
                    "Are You Sure to Close this Application?",
                    "Exit Confirmation", JOptionPane.YES_NO_OPTION,
                    JOptionPane.QUESTION_MESSAGE, null, null, null);
            if (confirm == JOptionPane.YES_OPTION) {
                System.exit(1);
            }
        }
    }

    public static void main(String[] args) {
        SwingUtilities.invokeLater(new Runnable() {

            @Override
            public void run() {
                ClosingFrame cf = new ClosingFrame();
            }
        });
    }
}

For the handling of this thing do:
if the user selects yes then use setDefaultCloseOperation(DISPOSE_ON_CLOSE); within the curly braces of that if else

if a cancel is selected then use setDefaultCloseOperation(DO_NOTHING_ON_CLOSE);

Consider example:

int safe = JOptionPane.showConfirmDialog(null, "titleDetails!",  "title!!", JOptionPane.YES_NO_CANCEL_OPTION);

if(safe == JOptionPane.YES_OPTION){
    setDefaultCloseOperation(DISPOSE_ON_CLOSE);//yes

} else if (safe == JOptionPane.CANCEL_OPTION) {
    setDefaultCloseOperation(DO_NOTHING_ON_CLOSE);//cancel
} else {
    setDefaultCloseOperation(DISPOSE_ON_CLOSE);//no
}

I've just tried this minimal test case:

import java.awt.event.WindowAdapter;
import java.awt.event.WindowEvent;

import javax.swing.JFrame;
import javax.swing.WindowConstants;

public class Test {

    public static void main(String[] args) {
        final JFrame frame = new JFrame("Test");
        frame.setDefaultCloseOperation(WindowConstants.DO_NOTHING_ON_CLOSE);
        frame.addWindowListener(new WindowAdapter() {
            public void windowClosing(WindowEvent ev) {
                //frame.dispose();
            }
        });
        frame.setVisible(true);
    }

}

If I keep the dispose call commented, and hit the close button, the window doesn't exit. Uncomment that and hit the close button, window closes.

I'd have to guess that something is wrong in your logic to set your "close" variable. Try double checking that.