Dear All, just a simple question. What happens when my mobile phone which im using DJI GO App for the live feed suddenly dies out of battery. The aircraft still on air and i believe controlling the aircraft will not be a problem unless the aircraft went out of my sight.

I believe you can use your remote RTH button and it will return safely just wait for it and don't panic.  Even with your tablet down the transmission will be dependent on your Remote Transmitter.   

There is no influence whether your app work or down.

As long as you still have green light on the controller you still have full control over your P3.  If your P3 is far away and/or you can't guide it back visually, press and hold Return to Home for a few seconds and the P3 should come back to you.  When it is ~30 feet up I'd advise quickly flipping the mode switch from P to A and back to P, then landing or catching the P3 manually rather than relying on auto-land.

the phantom works without a mobile device/app .. i believe that part is only for video, recording and other telemetry. you continue stick control until it comes back, or restart the app for video.

As others have said, you can fly your Phantom with the RC controller, as long as you can see it. Concerning the RTH button: it will work under these conditions, but keep in mind that if you push it twice (as some unfortunate posters have discovered) you will cancel the RTH command. In bright daylight it is not always obvious to see that the LED ring around the button is on.
Good flying!