iOS devices, including iPhone, iPad and iPod touch may exhibit an issue in which the Mail app displays the message “Cannot Get Mail – The Connection to the Server Failed” when attempting to retrieve new messages, especially from Microsoft Exchange servers.
Fixes
Move all items from inbox to a different folder. The most commonly successful fix for this issue is to move all items from the inbox into a temporary folder created on the server. It appears that problematic messages in the inbox can cause the error message.
Upgrade Exchange Server. You may need to apply a service pack to the Exchange server to which your iPhone is connecting. Some users have reported that they need to install Exchange Server 2003 Service Pack 2 to eliminate this error.
Change Exchange security settings. Some users have reported that they needed to turn on “Include inheritable permissions from this object’s parent” in the user’s security options in Active Directory.