Its electrical potential energy stays the same because it has the same electric potential. The reason why is that moving the charge towards X does not change the distance of the negative charge between the plates. The Electrical potential energy of a particle is the result energy by virtue of its position from the electrical fields produce by the plates both positive and negative. Since the charge is still equidistant to each other (assuming based from the diagram) no change in terms of electrical energy consumption or work was done.
