After pressing CMD+Option+Shift, look in the Edit menu. Is the first item "Undo Transform Again"?
Are you Transforming Again from the newly created layer copy, or the original layer?
Sounds like you are trying to preform this function on a "smart object". Convert the layer to pixels and it should work.
After Step 2: "I move the copy of the square to a new location and press enter to accept."
Do the marching ants still appear around the moved dupe? (They should)
Also, if at the end of Step 2 you press enter twice instead of once, the following Step will not repeat the image.