Simplest example of the issue is
javax/swing/ToolTipManager/Test6256140.java

This test displays a JFormattedTextField with a visible tooltip.
Robot does press 'a' and then

       robot.waitForIdle();

        if (!isTooltipShowning()) {
            throw new RuntimeException("Tooltip is not shown");
        }

        robot.keyPress(KeyEvent.VK_ESCAPE);
        robot.keyRelease(KeyEvent.VK_ESCAPE);

Problem is, almost always the test either hangs in robot.waitForIdle() and doesn't even enter that isTooltipShowning() or does it too fast so that tooltip is not visible yet. The first situation is typical for an individual test rerun.
Something should be done with that ASAP.

RULE "javax/swing/ToolTipManager/Test6256140.java" Exception java.lang.RuntimeException: Tooltip is not shown
RULE "javax/swing/ToolTipManager/Test6256140.java" Timeout none