Exchange email sync late for email, on time for calendar
One method I've found very useful for troubleshooting Exchange Activesync problems is to use the troubleshooting and connection logging functions built into the Touchdown Exchange client (30 day free trial app). It's helped me out with troubleshooting my Exchange connection in the past.

On the app's initial connection attempts to your Exchange/EAS server it logs the entire communication, with an option to save the logs for future reference. Once you've setup the connection there's a Diagnostics menu option on the main screen that can be set to log everything that happens between your phone and the server, with the option to attach the log to a new mail, or copy to the clipboard for use in other apps.