Unity Auto-update problem???

I don't think Unity is ever updating automatically. However, it will popup with a window saying a new version is out. If this window, for some reason isn't showing up for you. Simply go to:

Help > Check For Updates

This will show the popup update window, and if you got a older version, than the current active version, you'll be able to choose either "Download new version" or "Skip new version".

For future automatically popup window. Check the checkbox in the bottom right corner where it says "Check for Updates".

Hope that answers your question.