Hi Sebastien,
I believe this indicates an error in data transfer at the physical layer. One thing you can do is enable mmc debugging via linux kernel configuration (found under drivers->mmc support). This will produce lots of printouts with additional details. if this also does not give you any clues last thing you can do is connect with JTAG to the failed board and examine MMC registers. several of them contain bit fields indicating different types of errors that could occur during transfer.
regards,
Michael