Yes, removing files in /moodledata/backup/temp/ will free the space up and there shouldn't be a reference to that file in the mdl_files table ... didn't finish. Of course, am not the programmer of the routine so don't know exactly when the routine records info into DB.
An sql query of mdl_files for file names that end with .mbz should be the valid backups.
Do you have the option turned on for use course name in the backup file name turned on? Helps.
Am not sure ANYONE could give you a definitive answer without really knowing a lot about the remotely hosted system and the courses and course usage themselves.
Even if you turned on debugging .... automated backups won't have any screen to show errors and if there was a way to grab those errors, there becomes the problem of translating them into humanly understandable language!
Apache error logs *might* have some clues ... but I've seen remotely hosted systems setup where if something gets over limits, it kills whatever script AND doesn't report any error to the 'customer' ... that's something nasty but suppose it is assumed the OP knows what limits customer has purchased.
More and more am thinking sites of certain levels of usage need to be on dedicated server and one where the op has command line access. OR host with Moodle Partner ... OR get some 'semi-expert' help.
Afraid this sort of thing requires sluething.
I run/help admin RHEL/CentOS 5,6 servers - they have that can't *copy* larger than 4+Gig issue. And I have had to use command line and use 'move' to get those backups.
Situations are such that I cannot tell the digital photography teacher NOT to make camera assignments to 125 students requiring students to upload 6 photo types and for each photo type of 6 photos. That's just one assignment! See what I mean?
How about the teacher who decides to attempt a flipped classroom using nothing but Moodle?
Sooooo .... ???? We do what we must to support.
'spirit of sharing', Ken