Ok.
One of the "basic things" I refer to was, of course, trying manual backups. So, may I presume that you can manually backup the courses that return "unfinished" in the automatic backup? Do you use the same options (data included, files included...) in both types of backups? Try to manual backup a problematic course with everything enabled, to be sure that manual backups indeed works.
Check the backup log (admin menu-->reports-->backup-->click course name) for the exact description of the failed backup courses' procedure, specifically to know the stopping point. This can be a hint to the cause (an space or size problem if the error is writing to disk; a compression problemif the error is compressing...)
Try to increase php limits (execution time and memory limit, AFAIR, are the most relevant ones; see here). Try very high values, to discard or confirm its relevance.
Greetings.