it was because we were replacing the whole textfield's content with just that one sentence. Just add a + before =, like this:

Code:
myMessage.text += "Sarah says:";
and it should work, but if you want the caret (text selection cursor/pointer) to be aligned AFTER the inserted text, use this after the above code in the keyListener:

Actionscript Code:
Selection.setFocus(myMessage);
Selection.setSelection(myMessage.text.length, myMessage.text.length);

Hope this helps