Please ensure you are on 11d 7170 with latest service pack 5 and updates using live updates
When does the services stops and which service stop all the service or any particular service for backup exec ,please check that from windows services.
Is this happening when you are backing particular server or performing restore ?
Any particular event in event viewer during the time service stops
Need to give more information here to help you
11d 7170 sp 5 on Server 2003, this is not happen during backup or restore, and I have seen many times that backup exec job engine service is stopped.
details of event viewer are mentioned below:
Backup Exec Alert: Job Cancellation
(Server: "xxxxxx") (Job: "Backup_xxxxxx") The job was canceled because the response to a media request alert was Cancel, or because the alert was configured to automatically respond with Cancel, or because the Backup Exec Job Engine service was stopped.