This won't work with the built in platform behavior. You can either use physics or set up your own platforming events.
You could also possibly use a helper solid object. Upon collision, move the upper block up a pixel, and place a temporary invisible helper object of the same width below it, so that the fallen block is resting on this helper object rather than the moving box. When the moving box no longer overlaps the helper object, delete the helper object and the upper box should fall down. Haven't tested this myself though.