I posted a particularly popular comment on FB and got I inundated with push notifications for each comment. I tired turning off FB notifications in Settings, but they kept coming. I restarted my iPhone and iPad, and they still kept coming. Finally, in the app itself, there is a settings heading for notifications too. I stopped push notices here and they finally stopped. I would have throught the iOS Settings control would have been sufficient, but it wasn't.
I'm mentioning this because, this push setting must take as much, or more, resources as an email push notice. You might want to turn these off and see if that helps.