When the thinBackup is configured to backup to a directory outside of Jenkins home (/var/lib/jenkins) causes the backup to fail with a a wrong error, as per below log dump.

Checked permissions, and the jenkins user does have write access to the directory.

Mounting the directory to ie: /var/lib/jenkins/backups using --bind, and changing the backup directory from /var/backups/jenkins to /var/lib/jenkins/backups and the backup succeeds.

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13-Mar-2014 17:24:40 org.jvnet.hudson.plugins.thinbackup.ThinBackupMgmtLink doBackupManual
INFO: Starting manual backup.
13-Mar-2014 17:24:40 org.jvnet.hudson.plugins.thinbackup.ThinBackupPeriodicWork backupNow
WARNING: Do not wait until jenkins/hudson is idle to perform backup. This could cause corrupt backups.
13-Mar-2014 17:24:40 org.jvnet.hudson.plugins.thinbackup.backup.HudsonBackup <init>
INFO: No previous full backup found, thus creating one.
13-Mar-2014 17:24:40 org.jvnet.hudson.plugins.thinbackup.backup.HudsonBackup backup
SEVERE: Could not create backup directory. Backup cannot be performed.
13-Mar-2014 17:24:40 org.jvnet.hudson.plugins.thinbackup.ThinBackupPeriodicWork backupNow
SEVERE: Cannot perform a backup. Please be sure jenkins/hudson has write privileges in the configured backup path 'var/backups/jenkins'.
java.io.IOException: Could not create backup directory. Backup cannot be performed.
at org.jvnet.hudson.plugins.thinbackup.backup.HudsonBackup.backup(HudsonBackup.java:137)
at org.jvnet.hudson.plugins.thinbackup.ThinBackupPeriodicWork.backupNow(ThinBackupPeriodicWork.java:87)
at org.jvnet.hudson.plugins.thinbackup.ThinBackupMgmtLink$1.execute(ThinBackupMgmtLink.java:76)
at org.jvnet.hudson.plugins.thinbackup.hudson.model.AsyncPeriodicWork$1.run(AsyncPeriodicWork.java:53)
at java.lang.Thread.run(Thread.java:679)
13-Mar-2014 17:24:57 org.jvnet.hudson.plugins.thinbackup.ThinBackupMgmtLink doBackupManual
INFO: Starting manual backup.
13-Mar-2014 17:24:57 org.jvnet.hudson.plugins.thinbackup.ThinBackupPeriodicWork backupNow
WARNING: Do not wait until jenkins/hudson is idle to perform backup. This could cause corrupt backups.
13-Mar-2014 17:24:57 org.jvnet.hudson.plugins.thinbackup.backup.HudsonBackup <init>
INFO: No previous full backup found, thus creating one.
13-Mar-2014 17:24:57 org.jvnet.hudson.plugins.thinbackup.backup.HudsonBackup backup
SEVERE: Could not create backup directory. Backup cannot be performed.
13-Mar-2014 17:24:57 org.jvnet.hudson.plugins.thinbackup.ThinBackupPeriodicWork backupNow
SEVERE: Cannot perform a backup. Please be sure jenkins/hudson has write privileges in the configured backup path '/var/backups/jenkins'.
java.io.IOException: Could not create backup directory. Backup cannot be performed.
at org.jvnet.hudson.plugins.thinbackup.backup.HudsonBackup.backup(HudsonBackup.java:137)
at org.jvnet.hudson.plugins.thinbackup.ThinBackupPeriodicWork.backupNow(ThinBackupPeriodicWork.java:87)
at org.jvnet.hudson.plugins.thinbackup.ThinBackupMgmtLink$1.execute(ThinBackupMgmtLink.java:76)
at org.jvnet.hudson.plugins.thinbackup.hudson.model.AsyncPeriodicWork$1.run(AsyncPeriodicWork.java:53)
at java.lang.Thread.run(Thread.java:679)