Premature ENOSPC errors with XFS

Issue

The filesystems all had plenty of free space:

/dev/mapper/VolGroup01-opt_WebSphere_ISC_v70
                       8378368   6078708   2299660  73% /opt/WebSphere/ISC_v70
/dev/mapper/VolGroup00-var_adm_logs_migrate
                       8378368   1354808   7023560  17% /var/adm/logs/migrate

But the IBM Deployment Manager (dmgr) had an error trying to backup the files:

[12/9/13 6:26:03:476 EST]     FFDC Exception:org.eclipse.jst.j2ee.commonarchivecore.internal.exception.SaveFailureException SourceId:com.ibm.ws.management.application.EditApplication.exportApplication ProbeId:511 Reporter:java.lang.Class@3c0d3c0d
org.eclipse.jst.j2ee.commonarchivecore.internal.exception.SaveFailureException: Failed to save [ dojo131/dijit/themes/noir/noir.psd ]
Stack trace of nested exception:
java.io.IOException: No space left on device