I agree resetting the phone as new one is not a solution. I have tried everything but nope, it just ain't working. Just like Charlotte, it keeps getting push notifications after i close the app for 2-3 minutes, not after though. The issue must be connected to keeping the applications alive background. There's a setting for that in settings->general. But the thing is, I believe none of us changed any setting before this problem occurs. But something must be bugged to prevent apps staying alive in background if i'm getting messages after i close the app for 2-3 mins.Than its just shuts off itself. I have a 64GB phone and lots and lots of folders and settings and apps that i can't be bothered to set the phone as a new one. And yes, its NOT a solution, just a walkaround.
I hope someone can step up with a solution.
Cheers.