Hmmm.  That code was frustratingly close
to code that displays the problem (after
re-enabling the menu!).

Still - I was intrigued enough to continue
with it, and came up with this variant*.
I chose to:
- dump the JLabels for a direct 'paint()'
- lose the try/catch
- change the ActionListener for a KeyListener
- a number of other minor things I cannot recall.

* See how this works for you..
<sscce>
import java.awt.*;
import java.awt.event.*;
import javax.swing.*;

public class JRSCE
 extends JFrame
 implements KeyListener
{
 static final int COLS = 80;
 static final int ROWS = 22;
 String[][] grid = new String[COLS][ROWS];

 int columnX = 3;
 int columnY = 3;

 /**
  * @param args none.
  */
 public static void main(String[] args)
 {
   SwingUtilities.invokeLater(new Runnable() {
     public void run()
     {
       JRSCE thisClass = new JRSCE();
       thisClass.setDefaultCloseOperation(
         JFrame.EXIT_ON_CLOSE);
       thisClass.setVisible(true);
     }
   });
 }

 /**
  * build.
  */
 public JRSCE()
 {
   super("Use NUMPAD");

   GridPanel gp = new GridPanel();
   gp.addKeyListener(this);
   this.setContentPane(gp);
   pack();
   for (int y = 0 ; y < ROWS ; y++)
   {
     for (int x = 0 ; x < COLS ; x++)
     {
       grid[x][y] = ".";
     }
   }
   refresh();
 }

 public void keyReleased(KeyEvent ke) {}
 public void keyTyped(KeyEvent ke) {}
 public void keyPressed(KeyEvent ke) {
   switch ( ke.getKeyCode() )
   {
     case KeyEvent.VK_NUMPAD1:
       columnX--;
       columnY++;
       break;
     case KeyEvent.VK_NUMPAD2:
       columnY++;
       break;
     case KeyEvent.VK_NUMPAD3:
       columnX++;
       columnY++;
       break;
     case KeyEvent.VK_NUMPAD4:
       columnX--;
       break;
     case KeyEvent.VK_NUMPAD6:
       columnX++;
       break;
     case KeyEvent.VK_NUMPAD7:
       columnX--;
       columnY--;
       break;
     case KeyEvent.VK_NUMPAD8:
       columnY--;
       break;
     case KeyEvent.VK_NUMPAD9:
       columnX++;
       columnY--;
       break;
     default:
       System.err.println(
         "Use the numpad to walk!  " +
         ke.getKeyCode() +
         " / " +
         ke.getKeyChar());
   }
   /**
    * Bounds check to not "walk off the screen"
    */
   columnX = Math.min(COLS - 1, columnX);
   columnY = Math.min(ROWS - 1, columnY);
   columnX = Math.max(0, columnX);
   columnY = Math.max(0, columnY);
   refresh();
   repaint();
 }

 /**
  * Refresh the screen after each STEP.
  */
 void refresh()
 {
   for (int y = 0 ; y < ROWS ; y++)
   {
     for (int x = 0 ; x < COLS ; x++)
     {
       if (columnX == x && columnY == y)
       {
         grid[x][y]="P";
       }
       else
       {
         grid[x][y]=".";
       }
     }
   }
 }

 class GridPanel extends JPanel {

   static final int STEP=10;

   GridPanel() {
     setFocusable(true);
   }

   /**
    * The displayed dgrid of labels.
    */
   public void paintComponent(Graphics g)
   {
     for (int y = 0 ; y < ROWS ; y++)
     {
       for (int x = 0 ; x < COLS ; x++)
       {
         g.drawString(
           grid[x][y],
           (x+1)*STEP,
           (y+1)*STEP );
       }
     }
   }

   public Dimension getPreferredSize() {
     return new Dimension(
       (COLS+1)*STEP,
       (ROWS+1)*STEP);
   }
 }
}
</sscce>

--
Andrew T.
PhySci.org

Small stylistic notes, not related to your primary question:

"thisClass" is a very misleading name for a variable that is neither a class
nor points to 'this'.

Also, the convention for class names is that the first letter of each compound
word part is capitalized, not the entire identifier (e.g., "SwingUtilities",
not "SWINGUTILITIES") - so JRSCE should be "Jrsce", or better yet, a name that
actually describes something about the class, e.g., "FlickerDemo".

May I further suggest that you choose an indent level smaller than 8 spaces?
You run past the nominal 80-character line width much faster with such a large
indent.