Support

It depends on how you are triggering the backup.

If you are using the Front-end Baclup (Legacy API) or JSON API feature yes, you can. Check the Options page of the component. Change "When to send the email" to Upload Failed and customise your email so you receive the information you need.

When you are using a CRON job to run your backup you can configure your CRON daemon to send you the output of the CLI script by email. You can then use email filters to delete backup CRON emails which do NOT contain the word "WARNING". The idea is that failed uploads produce a warning when the upload fails.

For Scheduled Tasks there is no way I can think of. Then again, the number of people using Scheduled Tasks and needing this kind of feature seems to be zero.

Beyond that there is not much you can do. As far as Akeeba Backup is concerned, a failure to upload the backup archive is a regular Warning. You can optionally turn it into an error, but that means that the backup is failed (and the backup archive deleted) when the upload fails which is probably not what you want.

Trying to detect when a backup with an OK status is really a failed upload is a bit tricky because backup profiles are not set in stone. You can take a backup with a profile that has Post-processing set to None (so, it does not upload anywhere) and at a later time change that profile so it now has a Post-processing other than None. If we were to just check for all non-failed backups with local backup archives in every profile that has a Post-processing other than None it would be wrong because in the case I described above the backup would be flagged as having failed to upload. But it was never meant to be uploaded.

If I come up with a better way to detect this kind of backups I will include this as an option to the backup failure notification feature. It's something that I, too, would like to have.