Hi Ken!
Thanks again for the reply.
Directory permissions are correct, double checked them already...
I have some hope in the following: automated backup hasn't run for 2 years and I just turned it on. Like I said earlier, the whole process was taking about a month. The latest mail I've got is this one:
Summary
==================================================
Courses; 3385
OK; 102
Skipped; 530
Error; 0
Unfinished; 289
Warning; 0
Automated backup pending; 2464
Some of your courses weren't saved!!
Since 2464 automated backups seem to be pending, I'm going to be very, very patient to see what happens if everything has finished.
My guess is that mails like the above will appear first every 4 weeks, then every 3 weeks, then 2 weeks, and so on.
The backups that fail I will take 'as-is' and will look what's causing the errors (probably to much data in the course).
The Moosh thing is definitely worth exploring, but I will ask the makers if it will be possible to make it a 'normal' Moodle plugin. With normal I mean that it can be installed from the web interface (and without shell access to a server)