If emails will not syncronize with outlook while Exchange cached mode is turned on I have found the following solution.
https://support.microsoft.com/en-us/kb/2330226
The Microsoft KB states that this is for Outlook 2007 but this occured on Outlook 2016.
The solution is:
1. Close Outlook
2. <Windows key> + R
3. Type: outlook.exe /cleanips
Re-enable exchange cached mode if it was turned off.