Use your client to move the files instead of cutting and pasting in Explorer or whatever file browser you're using. That way, you move the data and keep the torrent pointed in the right location. If you don't really get it, think of it this way - you're pouring water into a cup and you can't see it (it's under the table or something), but your friend is helping you aim your stream. If your friend suddenly moves the cup and doesn't tell you, you're obviously not going to be pouring your water into the cup anymore. But if your friend tells you to move the cup, at least you know where to aim after moving it.
Most clients will also support automatically moving files into another directory once the torrent is done. This is my preferred way of doing it, so I don't end up opening incomplete files (which some clients hate; I remember Azureus/Vuze used to complain if I kept Explorer open in a directory it was downloading to, but that was years ago).
