I have the same issue with mail notifications. If I read and then delete an email BEFORE looking at Notification Center, I cannot get the mail to clear from Notification Center. I have to restart the phone to get it to clear.
Encountered this with Telegram on my iPhone 6s running iOS 9.0.1. Tried to dismiss the notification via the clear button, but it stayed in NC. Tried with a swipe on the notification itself, and tried using the x there, but same result. Fixed itself with a hard restart