Sounds as if you've got the whole thing copying 3 times?... that would account fro the looping back to the beginning, and 3x13GB (39GB) for a 3 hour file.
I've just checked my instructions with a DV.AVI file from my camcorder, and just for fun 'appended' the same fileon to the end. As a 'direct stream copy', it was, as I expected, exactly twice as long, and played back the same thing twice.
Can you try and just append one segment to your original segment, and make sure that just plays back once?. It should also be exactly the same length as the two separate files.
You can check the exact details of any video file using the freebie
MediaInfo , just to check it's not being changed at all.......