There are a couple of ways to see what is happening with your backup jobs.
In the vSphere Web Client, you can go to Hosts and Clusters, then pull up your VDP appliance VM, click on the Monitor tab, then check Tasks for the backup job and it should display details about what occurred.
If for some reason that does not provide enough information, you can also SSH / putty into the appliance to check the proxy logs.
In the /usr/local/avamarclient directory, you can do an 'ls -ltR | less' to see a list of the most recent jobs and the logs associated to them.
Once you have located the log of the backup job you want to check, note which proxy it ran under (should display directory name prior to list of contents).
cd to the proxy directory and then you can view the log file of the backup job. The log you are interested in would be named "JOB_NAME_vmimagew.log" or "JOB_NAME_vmimagel.log" (w for windows VM, l for linux VM)
You can search on "completed" within the log to see if the job completed successfully. If so, it will give stats about how long the job ran, ow much data it backed up.
If your job failed to complete, then this log should provide more insight in regards to what occurred.