When the plate spacing is large the capacitor system is storing more energy than when it is small.
If one manually changes the spacing, where does the additional energy "come from" as the plate spacing increases?
Energy is only conserved in a closed system, if there are external forces you must account for the work done by them.
Remember that the plates are oppositely charged, and thus they attract. If you wish to pull them apart, you must apply an external force. As the plates are moving, there is displacement and net work is done on the system. This work is stored as the potential energy of the capacitor.
Think about the same question when applied to a spring -- where does the extra energy come from when you stretch a spring? Or when you pick a ball up and place it at a higher elevation. Both of these situations require the experimenter to do work on the system.