I've worked it out. You can specify when the component removal
happens by using a mx:RemoveChildAction tag:
<mx:Style>
@font-face {
src: local("Arial");
fontFamily: myArial;
}
global {
fontFamily: myArial;
fontSize: 15
}
</mx:Style>
<mx:transitions>
<mx:Transition fromState="" toState="A">
<mx:Sequence target="{lblMessage}" duration="2000">
<mx:Glow alphaFrom="1" alphaTo="0" />
</mx:Sequence>
</mx:Transition>
<mx:Transition fromState="A" toState="">
<mx:Sequence target="{lblMessage}" duration="2000">
<mx:Fade alphaFrom="1" alphaTo="0"/>
<mx:RemoveChildAction/>
</mx:Sequence>
</mx:Transition>
</mx:transitions>
(Note: I've also embedded a font to allow the Fade effect to work
properly)