Found keyboard navigation not working in Solaris as well as Windows platforms if the popup menu boundaries exceed the boundaries of its caller. As a result, could not use mnemonics and also could not cancel an opened (using mouse) popup menu using 'Esc' key.

Code used:
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import java.awt.*;
import java.util.*;
import java.awt.event.*;
import javax.swing.*;

public class PopupMenuTest extends JFrame {
  private Label label = new Label("Click here for popup");
  private JPopupMenu pMenu;
  private JMenuItem mItem;
  
  public PopupMenuTest() {
    //label.setPreferredSize(new Dimension(250, 250));
    
    pMenu = new JPopupMenu();
    
    mItem = new JMenuItem("One");
    mItem.setMnemonic(KeyEvent.VK_O);
    pMenu.add(mItem);
    
    mItem = new JMenuItem("Two");
    mItem.setMnemonic(KeyEvent.VK_T);
    pMenu.add(mItem);
    
    mItem = new JMenuItem("Three");
    mItem.setMnemonic(KeyEvent.VK_H);
    pMenu.add(mItem);
        
    label.addMouseListener(new MouseAdapter(){
      public void mousePressed(MouseEvent e) {
        pMenu.show(label, e.getX(), e.getY());
      }
    });
        
    getContentPane().add(label, BorderLayout.CENTER);
  }
  
  public static void main(String s[]) {
    PopupMenuTest p = new PopupMenuTest();
    p.setVisible(true);
    p.pack();
  }
}