Flip Case? and Battery tips?

Anybody here with the OEM Flip Case? It was working well with power save (on). Where If I closed the flip case, the phone instantly locks the screen. I like this cause instead of reaching for the power button, my phone locks itself. Which is very cool when you use power amp since you can get full access to the main controls on the lockscreen

For some reason, my screen doesn't lock itself whenever I close the flip cover. It also leaves the edge screen on.

Help any tips? I am trying to squeeze more than 13 Hrs off this phone. I can get about only 5 hours of screen time and thats not gaming. thats writing notes, facebook, messaging. Thats it. The battery life on this phone is sad, even with stock KitKat