Backup job doesn't write backup when run on schedule
Does anything show up in the backupset tables for the missing backups?

SELECT  TOP 5
        bs.database_name, 
        bmf.physical_device_name,
        bs.backup_finish_date,
        BackupSize = CONVERT( VARCHAR( 16 ), 
            CONVERT( DECIMAL( 18, 4 ), bs.backup_size * 1.0 / 1024 ) ) + 'KB',
        AfterCompression = CONVERT( VARCHAR( 16 ), 
            CONVERT( DECIMAL( 18, 4 ), bs.compressed_backup_size * 1.0 / 1024 ) ) + 'KB',
        bs.type
FROM    msdb.dbo.backupset bs
INNER JOIN msdb.dbo.backupmediafamily bmf
    ON  bmf.media_set_id = bs.media_set_id
WHERE   bs.database_name = '&lt;Your Catalog Here&gt;'
    AND bs.type = 'D'
ORDER BY bs.backup_finish_date DESC;


I would wager you are right that it's not a permissions issue, as if it was, the job history would indicate it.  Similarly, if the network path was simply unavailable at 7:00AM, there'd be something in the job messages about it, even if the jobstep itself was set to always report success.

SELECT  ji.name, ji.step_name, ji.step_id, ji.run_date, 
        ji.run_time, ji.run_status, ji.on_success_action, ji.on_fail_action, ji.message
FROM (  SELECT  sj.name, sjs.step_name, sjs.step_id, sjh.run_date, sjh.run_time,
                sjh.run_status, sjh.message, sjs.on_success_action, sjs.on_fail_action,
                Ordinal = ROW_NUMBER() OVER (
                    PARTITION BY sj.name
                    ORDER BY sjh.run_date DESC, sjh.run_time DESC )
        FROM    msdb.dbo.sysjobs sj
        INNER JOIN msdb.dbo.sysjobsteps sjs
            ON  sjs.job_id = sj.job_id
        INNER JOIN msdb.dbo.sysjobhistory sjh
            ON  sjh.job_id = sj.job_id
            AND sjh.step_id = sjs.step_id ) ji
WHERE   ji.Ordinal &lt;= 5
    AND ji.name = '&lt;Your Job Here&gt;'
ORDER BY ji.run_date DESC, ji.run_time DESC,
    ji.name, ji.step_id;


I'm guessing it's some subtle difference between the successful jobs and the one that's behaving oddly, like a conditional that's getting evaluated differently by the agent or similar code issue.