It isn't related to the file not found error message. I get the same thing, but I can get my games from the Wii.
I think the problem is that there is an interruption in the signal between the Wii to the router or from the pc to the router (Or there is a bug in your system that temporary halts your connections and that stops the download). Did you try it more then once, as in does it always stop at 3.17GB? If it does, then I'm guessing it might be a problem with the disk or the computer is closing the connection (Which I never really have heard of, but it is a possibility).
Does the program give a specific error in regards to premature terminations, or does it still say Connection finished?