Edit 20100220:
It seems to be possible to make a backup of the standard persistent image, compress it, and have it copied back at boot time if something has gone wrong with the running image. ...
I looked inside /init (Knoppix 6.2.1) and found the code for updating the system:
Code:
# Check for updates on-disk, install them if necessary.
ls /mnt-system/KNOPPIX/update*.zip /mnt-system/KNOPPIX/update*.tar.gz /mnt-system/KNOPPIX/update*.taz 2>/dev/null | while read update; do
 if [ -r "$update" ]; then
  message -e "\r${CRE}${GREEN}${UPDATING} ${YELLOW}$update${NORMAL}"
  case "$update" in
   *.zip) ( cd / ; unzip -o "$update" >/dev/null 2>&1 ) ;;
   *.tar.gz|*.taz) ( cd / ; tar -zxf "$update" >/dev/null 2>&1 ) ;;
  esac
 fi
done
As far as I understand the code, one has to create an ordinary zip or tar.gz archive inside the running system and place this archive in the KNOPPIX directory. The archive will be extracted into /.

For example, I could run KNOPPIX from the live cd and make all the necessary changes. Then I would create the update-special.tar.gz archive with my configuration files which is copied to a flash device with an installed KNOPPIX on it. I would delete an existing persistent image and boot the system from that flash device. After the creation of a new persistent image I would get a KNOPPIX with my special configuration. (I tried this with a backup of may /home/knoppix and it worked fine.)