Hello,
DLO wont continue backup from where it stopped. You will need to make sure that adequate space exists on the Local user data folder (LUDF). The LUDF is essential as dlo stores each user's data in two places to provide protection and restore even when the computer is disconnected from the network.
For more information on this option and its functioning, refer to chapter J on page 1181 in the admin manual for backup exec 9.1. Here is the link for the download:
http://support.veritas.com/docs/266190
Do update on this issue.
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Regards.