A mid-range Asus phone with a 4,850mAh battery has shown up on TENAA's website. The combination of an HD screen and high-capacity battery should mean best-in-class endurance, even under heavy use.
http://www.notebookcheck.net/Asus-X00GD-is-a-mid-range-smartphone-with-a-high-capacity-battery.189718.0.html