OSX Lion 10.7.1 - Safari, Textedit or Stickies in separate Mission Control Desktops
If the item you're trying to move springs back then it's most likely already on the space / desktop you're trying to move it to.

You can also try moving something to another desktop in ways other than Mission Control:


Let's say you already setup two spaces, and you want something from
space one onto space two; Just drag the window of whatever it is to
the edge of the screen and hold it there until it moves over to the
other space.
Another way you can do this is to simply open whatever application or
file you want in that particular space.


Apps are automatically assigned to the Desktop / Space where they are launched for the very first time. You change this by Control clicking the apps icon in the
   dock, and assign to None.