Well I had the same exact requirement, and Robot class is perfectly fine for me. It works on windows 7 and XP (tried java 6 & 7).
public static void click(int x, int y) throws AWTException{
Robot bot = new Robot();
bot.mouseMove(x, y);
bot.mousePress(InputEvent.BUTTON1_DOWN_MASK);
bot.mouseRelease(InputEvent.BUTTON1_DOWN_MASK);
}
May be you could share the name of the program that is rejecting your click?