Does the dvd play correctly all the way through? Are there any scratches or dirt or smudges near the edge of the disk?
What are you using to copy the disk? Are you ripping to the hard drive using the built in ripper within AnyDVD?
Have you tried running AnyDVD in the background and making an ISO of the dvd with ImgBurn? (you will get a warning message saying AnyDVD interferes with verification, but you can ignore this if not running verification of the image after making the ISO). If you can make the ISO successfully on the hard drive, you can then burn to a disk.