How old is the phone? The battery life performance will degrade over time.
With iPhones it's not usually apps in the background that cause these sorts of problems as iOS has quite strict rules about what apps are allowed to do in the background and how long they are allowed to run for in the background.
It could possibly be due to app updates being installed, or if an iCloud backup was started while the phone was plugged in it could have continued after it was unplugged and used quite a bit of power for that.
edit: based on what you've said above, try switching off background updating for Twitter and see if that improves the situation.