The Sony Xperia Z has a battery STAMINA mode, which gives you at least 4 times longer standby time, so there is no worry about running out of power. However, several reports reveal that the STAMINA power saving mode does not functioning properly with the latest 10.1A.1.434 firmware. Even if you switch on the STAMINA mode there will not be seen any change.
Though there is no any official fix available from Sony yet, you can temporarily fix the issue by clearing the data from the ‘Eco mode controller’. Here is how it is.
Go to Settings -> Apps -> All apps.
Scroll down until you see a program called “Eco mode controller” and tap it.
Now, tap Force stop and then tap Clear data.