Jooel is spot on except that ListIndex is a zero-based and starts at zero and ListCount starts at the number one. This gotcha got me as well (lol) ... so whats happening is that you add the first item and its ListIndex is zero - but the ListCount is one (there is no index one yet) - and it keeps on going like this never being able to select that last added entry. Bottom line is that you have to substract one from the ListCount value like this:

$ListBox.ListIndex = $ListBox.ListCount-1

-Shawn