It might also be a visualization problem - if the piece is physically standing in the new square, it's easier to grasp the situation than if you have to imagine the piece on the new square (and imagine the old square without the piece).
This used to be a big problem for me - I tried to visualize what could happen after a certain move, I said to myself: This piece is protected by the bishop on c3 (for example), and not thinking about that exactly that bishop was the one I was about to move (and after the move of course would be no longer protecting what it was protecting right now :)
On more than one occasion I have made a move, and almost instantly I recognize what will happen either more clearly or more deeply than when I was thinking about the move. It seems like the active thinking part of the brain is latching on to an idea too strongly and as soon as it lets go something else kicks in.
Has anyone else experienced this? What's the cure? Walk away from the board for a minute before moving?