I also have this problem on my iPhone 6.
It only seems to affect emails, all other notifications clear ok. My notifications in the slide down centre are ordered by day, so i ended up with a week's worth of email notifications which wouldn't clear.
I have managed to clear them by switching off email notifications in the slide down centre, then changing the ordering to 'Manual'. This seems to clear out all old notifs, and since i've switched off email notifs it doesn't attempt to re-add them in the new order.
I'm going to keep them switched off in the notifs centre as i get so many it's just as easy to open the mail app to see what i have.