Disable it.
Facebook is already disabledDelete the application facebook.
Facebook and FB Messenger are pretty much ALWAYS ON. Disabling Facebook was Step 1 for me; it helped a bit. But now that I figured out that Messenger is a battery drain too, I changed settings to have FB text me when I get a Messenger message. If you have a limited text package then perhaps this might not be an option for you; basically I get the text, then I open up Messenger in my mobile browser...
cheers/dom
Does it text you for every message you get though??