I have the battery problem on my Sony Xperia J (ST26i) since i bought it months ago. The battery life was really horrible as sometime it can only last half day even though without too much data on my phone. The problem finally fixed not long ago. I have tried everything i know like turning wifi/gps off, dimming the brightness, and tried the saving mode or power saving apps without much improvement. Not long ago, I once happened to turn off the background data and auto-sync, my phone last through one whole day! I have an addictional battery from mpj which provides some extra power also make it last over one day, but with the original battery is my first!! I think probably the reason is that I am living in an area where signal not good so sync/update my phone/apps would take extremely long time.