I several problems with Exchange Sync since upgrading to iOS8, one of which is similar to you.
I have an iPhone 6 and an iPad 3rd Gen. Both of them currently running the latest iOS 8.1.
I think the issues started with 8.0.1 or 8.0.2 upgrade but I'm not 100% sure, because I became aware of them over time.
Both devices are configured to sync Mail, Contacts, Calendars, Reminders and Notes with an Exchange 2013 account.
Both devices are set to Push Exchange data (incl. Inbox and a sub-folder of my Inbox).
My iPhone 6 is set to show Mail in notification center: Badge / Show on Lock Screen / Banners / Show Previews (it is important to me to know as soon as an email comes in).
My iPad seems fine.
My iPhone 6 on the other hand shows the following problems:
1. Calendar is no longer syncing (it is still showing Cal Items that were synced before whatever upgrade caused the problem, but new Cal Items are no longer syncing) (not sure whether Contacts etc. are still syncing, as I don't often enter/edit Contacts)
2. Emails are no longer pushed (they are fetched as soon as I enter the "Mail" app)
Both of these issues are critical. If someone from Apple could respond that would be great.