In a post on Facebook, Ari Grant, engineering manager for iOS at Facebook, has confirmed that the Facebook app was affected (among other bugs) by background audio issues which caused high battery consumption.
The second issue is with how we manage audio sessions. If you leave the Facebook app after watching a video, the audio session sometimes stays open as if the app was playing audio silently. This is similar to when you close a music app and want to keep listening to the music while you do other things, except in this case it was unintentional and nothing kept playing. The app isn't actually doing anything while awake in the background, but it does use more battery simply by being awake. Our fixes will solve this audio issue and remove background audio completely.
From what I've heard, today's update to Facebook for iOS has removed the background audio permission completely. Facebook is working on more fixes, which, as Grant also mentions, include improvements to the app's network code.
At this point, I don't think it's productive anymore to speculate on how long the problem has been around. I'm glad that Facebook has publicly acknowledged issues that were affecting battery life on iOS and it's good to see fixes being released to address them.
I'm going to reinstall the Facebook app and see how it goes.