If the backup directory does not exist, the backup service fails. Even though there is a warning in JIRA's log file, I don't find this sufficient for such an important functionality.

I would suggest the following important improvement:
Make Jira create the directory if it does not exist.
If unable to create the directory, generate an email warning to the jira administrators in order to have the problem identified and fixed.

As everybody knows, having a backup may be crucial for if you experience a harddrive failure........

I found a quite similar request JRA-7912 where another backup failure is discussed, though I want to adress the directory problem specifically as this can be easily fixed (simply creating the directory will in most cases fix the problem).