Page 2 - Schedluled cron job stpped working

Gah, sorry - somehow missed your previous post!
Those crontab outputs explain what is going on. The back.sh script is being run as user basil, whcih means that when it comes to copying the backup file to the target location you do not have the correct permissions to access the contents of the directory (it is rwx by root only).
So, what do we do? Hoping it is ONLY the directory permissions which are fouling things up we have a range of options which, in not particular order of 'good', include:

a) change ownership/permission on target directory.
b) have the back.sh script run by the root user
c) set up sudo to permit the file copy to be done by root
d) use setuid on the back.sh to have it run, effectively, as root

A lot of the answer will depend upon what else the Dropbox directory is for. If it's JUST for your backups for this then I'd be inclined to:

which will permit the basil user full access and thus allow the file operations being done and give root access via the group permissions (not that the root user really needs this).
Also, I'd be inclined to:

which will make things 'look' better, it just reinforces the point that the script is run (and owned) by the basil user.

I only performed the first part of your suggested "fix" - and that has got cron working again, when I manually do a "run now".

I really appreciate the time and effort you've taken. So please don't apologise.
I could still be "up the creek without a paddle" if not for your persistence and advice.

Thanks heaps.

Glad it's working for you, but more to the point I hope you know why it is.

Silly question - you didn't happen to have an external disk or NAS or something similar mounted at /root/Dropbox did you? Reason I ask is that the thing that was mounted may well (probably would!) have had the correct permissions on it.

No never any external device connected. I'd suggest it "just happended", but I know that can't be true.

As for knowing what's going on....

chown basil - giving usr basil ownership of the required directory
chmod g+rwx - adding group permissions for the directory to rwx

Again, I appreciate your efforts and approach.