I have exactly the same problem, despite trying a factory reset and reinstalling the firmware fresh. using Facebook app doesn't seem to make much of a difference, it's rubbish anyway. I do restrict background use for the Facebook app though. 3 hour screen on is absolute maximum I can ever achieve now and I normally have to charge when I get home from work. I used to get a good hour more than that and never needed to charge during the day. its the primary reason I will change my phone after a year as I don't think the battery will last two