Backup & Migrate scheduled backup silently fail
It is because you are using buggy module with known issues. This has nothing to do with BOA nor Aegir. There is a reason why we have removed this notoriously buggy module from BOA recently. You should report any such issues in the backup_migrate issue queue on drupal.org - and you may find them reported already, in fact.

This module may still be useful, but only if you follow its issue queue and use release which happens to work. The regressions rate in this module is way too high for us, so we no longer include it by default. Just one example:
https://drupal.org/node/1997354
and a fix:
https://drupal.org/node/1997354#comment-7426824