Really don't know what to suggest then, never seen that before. LMCE uses CDParanoia to actually do the rip, and this has extensive error correction and scratch removal stuff, which is why it rips so slowly. Perhaps you could try ripping these at the command line to see what kind of error-out you are getting when it fails. You may have to grep all the scripts for the exact command it runs (or a dev might chime in here) then simulate the same command with more verbose logging.
BTW - in the past I have had numerous problems ripping DVDs to remote file shares (XP), just bombs out shortly after starting. Never found out why, it doesn't seem to do it any more, and it was DVDs not CDs, but maybe give that a try - rip to the core...