I backed-up my copy of ResidentEvil:A without any problems. I used the latest version of CloneDVD 2543 and AnyDVD 4301 (all on default settings).
HOWEVER, I only backed up the MAIN movie. I did NOT try backing-up the whole DVD. I tested the backup on my PS2 and it worked fine.
Unfortunately I don't have any solution for people with problems. Maybe you can try backing-up just the main movie and not the whole disc.
I used a Plextor 708 (firmware 1.08) and Ritek a G04 4X DVD-R disc for the backup. I used a generic Pioneer DVD-rom drive for reading (firmware hacked to read all-regions).
Hope this helps.