iOS 7 email issues

After upgrading my iPhone 5 to iOS 7, emails are either not being sent, or it takes 20-30 minutes to leave the device. The messages are not sitting in the Outbox and don't show up in the Sent folder until 20-30 minutes later, if at all. This affects all email accounts (Exchange, Gmail, etc.).

I have deleted/re-added the email accounts, restarted the device, and reset the network settings. Upgrading to iOS 7.0.2 did not help. Any suggestions would be greatly appreciated.