I'm also seeing the issue where a DVD will begin to rip, but after some time it is aborted.
I'm not sure if it is at the 2gb mark, but this may be the case as the last time I checked it, about 1gb had been done and next time I looked the ripping process had been aborted.
This happened for a number of different DVDs, all of which seems to play fine on the MD when running from the disc.