Did this actually fix your issue though? I managed to get it back into Notification Centre by doing a reset (power and home buttons) but this didn't actually cause the notifications to come through. The iPad received them fine, but the iPhone didn't.
I'm going to hazard a guess and say Paper has screwed something up server side for iPhone.
At this point I can't say for sure they are coming through as I fixed them last night (during the night) so there were no new posts and now everybody is at work. This afternoon people should start posting and I will see if they come through. All I can say for sure at this point is it now appears in notifications.