When smartphone is unable to establish a connection with a Microsoft ActiveSync server, the first step will be to check if the ActiveSync server is actually available.
If the ActiveSync server is exposed to the Internet, it is possible to use Microsoft Remote Connectivity Analyzer tool:
https://testconnectivity.microsoft.com/
If Active Sync connection is not open on the corporate firewall, it is possible to test it internally.
Exchange 2003
Access the following link: https://<ActiveSyncServerURL>/OMA
Exchange 2007 to 2013
Access the following link: https://<ActiveSyncServerURL>/Microsoft-Server-ActiveSync
There will be no actual page open, but an error or a logon window pop-up. It should not be a message like: Page cannot be displayed.
Retated topics: http://austit.com/faq/258-owa-sharepoint-active-sync-stopped-working