When I installed 8.0 on my 5S, all my notifications stopped. I kept 8.0 on the phone a few days and then went back to 7.1.2.
My mail.app frequently doesn't get push notifications from my exchange accounts. They all come in when I turn the screen on...
They all kinda stopped for me. I tried restarting but nothing yet. I was getting them all day but they stopped about 2 hours ago.
I'm hoping 8.0.2 fixes the notifications for me. Now I just have to work up the courage to download it