Andy Galbraith diagnoses an “ACTIVE_BACKUP_OR_RESTORE” issue:
The way FULL backups work in SQL Server, the transaction log is not released for re-use during a FULL backup, even if regular LOG backups are occurring or the database is in SIMPLE recovery. This is due to the fact that the portion of the LOG that is used during the FULL has to be persisted during the FULL in order to be backed up at the end of the FULL – that is, the FULL backup includes the data at the start of the FULL (23:30) *plus* the LOG used until the end of the FULL (in the case of the 12/04-12/05 backup, the LOG used from 23:30 to 07:11). This is the meaning of the ACTIVE_BACKUP_OR_RESTORE message – the LOG is waiting for the end of the active FULL backup before it can be released for re-use, which in this case was causing the LOG/LDF file to grow to fill its mount point.
This is interesting analysis and a reminder that even though you’re in Simple recovery mode, SQL Server still uses a transaction log and it’s just as important.