Everything from the /var/log dir around the times of the crashes looks normal. Hard drive in question is a 45 gig with 86% used (according to df), so disk space shouldn't be the issue.
14% free of 45 gb is 6.3 gb free
how big is the large directory
and how large is all the data you're backing up?
du -hs /the/large/dir/where/it/crashes
du -hs /
is there maybe a softlink in a directory that points to directory back.. use a command line switch to ignore softlinks..
and a good thing to try is to audit the amount of available diskspace on the slackware server..
add this line
1 * * * * df -h >> /var/log/diskspace
now try backing up again and when it crashes reboot and check the file... the last line will tell you enough about the available disk space..