I always wrap it twice, I believe this is due to how the page the loaded with the panels

<apex:outputPanel>
  <apex:outputPanel id="nonePanel" rendered="{!debrief.Stage__c == ''}" >
                None block
  </apex:outputPanel>
</apex:outputPanel>

Try it with one of your picklist values and if it works do it for the rest..

I always wrap it twice, you cannot rerender a vf component that hasn't already been rerendered

<apex:outputPanel>
  <apex:outputPanel id="nonePanel" rendered="{!debrief.Stage__c == ''}" >
                None block
  </apex:outputPanel>
</apex:outputPanel>

Try it with one of your picklist values and if it works do it for the rest..