When you deploy the application the statistics are "OFF" by default. When the appnode and applications are in "Running" state you can set statistics "ON" for running application and appnode. Once you set statistics "ON" deployed application it will remain "ON" until you mark it "OFF". However it would seem that by each redeployment of application (deploy of newer version), statistics go "OFF". 

The stats will be reset for an appnode only when there are no application deployed to it. So for example, let's say you have 2 applications App1 & App2 deployed to an appspace & you have enabled stats on the appnode. Now when you undeploy App2, the appnode will still have stats enabled. However when you undeploy App1 now, the stats will be reset for the appnode.