As some, if not all, of you have experienced, the Outlook notification does not come up if you have set up Rules/Filters to go into folders (vs the Inbox).
In order to turn them back on, the “Display Desktop Alert” action must be explicitly set for a Rule.
Steps to turn this on:
1. Go to Tools->”Rules and Alerts…”
2. Choose the rule you would like to modify and click on Change Rules->”Edit Rule Settings…”
3. Click on the Next button and in the “Select action(s)” step (after Select Condition), scroll down and check on “Display a Desktop Alert”.
I have not spent the time yet on finding out how to turn this attribute on globally or modify all rules to have a certain attribute set so feel free to share if you know or discover how to. For now, I had to set it manually for each rule. :(