Thanks for uploading. Since I'm the owner of the site, I can see the flight record in my site logs.
It looks like you took off at 5:38:34PM at about 53% battery.
Everything was fine until, at 5:39:39PM, there was a communication error between the battery and the motherboard (this can happen if e.g. the tiny contacts on the side of the battery aren't making good connection with the Phantom). At that point you had 51% battery left. Because battery communication was lost, the battery reading got stuck at 51%, even though you were still in the air and guzzling up the battery. The battery voltage at that point was 14.659V.
After another ten minutes of flight, at 5:48:56PM, the battery voltage had fallen to 13.469V, which is below the flight controller's critical low battery voltage threshold (presumably 13.5V). Your Phantom went into autoland mode and came down slowly in the water.
I conclude that the actual battery itself was OK and didn't fail. The battery communication error is definitely a fault in either the smart battery circuit or the Phantom itself. I guess one interesting question is, did the app warn you that battery communication had failed?
And yes, this is a great reminder that if the battery percentage stops decreasing, we need to watch the battery voltage carefully - if battery communication is not working, we might have less battery left than the app claims.