I had this, too. When I was collecting things on a map (that is using the both battery-drainers display and GPS).
You could try the following to rule out GPS as battery-drainer: Go to “Settings” - “Location” and turn the switch off or set “Mode” to “Battery saving”.
If the Facebook app is installed, uninstall it and use Facebook via browser. There are many reports that the Facebook app is causing severe problems on the FP2 and in general.
If your phone battery still drains so quickly, you should remove the SD card, reset your phone to factory defaults and run the phone without any user-installed apps. (If then the battery is drained unusually fast, then your phone is defective and needs to be replaced.)