OK, the real answer....
That reply box smilie window contains 24 smilies. In the big listing of all smilies, there are 159 smilies currently, each of them is assigned a display order number (1-10) which gives them an order in which to display.
I just checked, and there were 25 smilies given the order number of 1...And they were all vying for the 24 spots on that display. One always loses out, but because of that, they were kept in rotation.
So I changed this guy
to display order 2, and now that there are only 24 (with a display order of 1), they should stay put.