My Server-Backup-Manager is telling me there was a problem with the Backup (only full backups) once I try to download the backup log file this is empty (0 Bytes).
The log file can look "empty" if the number of errors in the log is very high. In that case timeouts occur before the whole file is read and processed by Plesk. We ran into that situation recently. In that case you can always go into /usr/local/psa/PMM/logs and descend into the backup-2017-... directory to access the files in question directly.