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A couple questions/comments:
When you define a backup you end up with a couple options: "One time backup", Scheduled with no triggers, and Scheduled with triggers. It sounds like you're setting up one time backups.
Ghost's services will run in System context and therefore do not require you to be logged in to run a scheduled backup event. In fact, you can also set a trigger for a backup to occur when a user logs off.
Whenever an error occurs in ghost an entries is written to the Application event log in Windows. If you are coming back and finding no events, missing entries, etc then something is being modified outside of Ghost and this is not expected behavior.
Out of curiosity do you have GoBack installed? Do you have Auto-Revert enabled? Where are you setting up your backup location to? Could you set up a scheduled backup and copy the summary page contents and paste in a reply post?