i had this issue on my ipad mini back on 7.0.2. when i upgraded to 7.0.3 OTA, it still didnt fix it. i tired updating via itunes, still didnt work. the only way to fix it was to restore as new. pain in the butt, but i tried literally every suggestion i found on the internet, and i searched for hours. you will most likely need to do the same.
Won't fix it. I did the same thing, waited for 7.0.3. Once I updated, the notification stuck again. I had no choice but to restore and set up as new. I tried restoring from back up and that brought the badge back. For me, I'll never do OTA again.