https://wordpress.org/support/topic/problems-with-the-db-backup?replies=6
https://wordpress.org/support/topic/warning-fopenhtaccess-functionfopen-fwrite-fclose?replies=49
Do this first: Go to the DB Backup page >>> click the Create Backup Jobs accordion tab >>> use the Rename|Create|Reset Tool by clicking the Rename|Create|Reset button to see if the problem is related to the DB Backup folder name.
Next do this: check the permissions and Ownership of the /wp-content/bps-backup/ folder and all subfolders. Change the permissions or Ownership if needed. If you are not sure how to do that then ask your host to check this.
Next do this: uninstall and reinstall the BPS plugin.