This probably is OS dependant - I'm on Windows 8. When I press F10 it registers, but after that all function keys are ignored until I either press a non-function key or F10.

Example code to show what I mean:

1. import java.awt.event.KeyEvent;
2. void setup() {
3. }
4. void draw() {
5. }
6. void keyPressed() {
7.   switch(keyCode) {
8.   case KeyEvent.VK_F1:
9.     println("F1");
10.     break;
11.   case KeyEvent.VK_F2:
12.     println("F2");
13.     break;
14.   case KeyEvent.VK_F3:
15.     println("F3");
16.     break;
17.   case KeyEvent.VK_F4:
18.     println("F4");
19.     break;
20.   case KeyEvent.VK_F5:
21.     println("F5");
22.     break;
23.   case KeyEvent.VK_F6:
24.     println("F6");
25.     break;
26.   case KeyEvent.VK_F7:
27.     println("F7");
28.     break;
29.   case KeyEvent.VK_F8:
30.     println("F8");
31.     break;
32.   case KeyEvent.VK_F9:
33.     println("F9");
34.     break;
35.   case KeyEvent.VK_F10:
36.     println("F10");
37.     break;
38.   case KeyEvent.VK_F11:
39.     println("F11");
40.     break;
41.   case KeyEvent.VK_F12:
42.     println("F12");
43.     break;
44.   }
45. }

Potential solution here? I don't really follow what's going on though:
http://www.dreamincode.net/forums/topic/268248-f10-blocks-other-action-keys/

Anyone with a better understanding of Java able to help out?