How can I sync an Exchange 2003 inbox to an Android 4.x device? I have ICS 4.x and I'm trying to get the default email client to connect to a MS Small Business Server 2003.

The client will sync all folders but Inbox. I get the error message "Couldn't Open connection to Server". I'm able to send emails, any clues?
I was just suffering from the same issue with an Exchange 2010 server. The problem was server-side not client-side.
Upon investigating the event log for the Exchange role, I noticed the following error entry:

Exchange ActiveSync verfügt nicht über ausreichende Berechtigungen zum Erstellen des Containers &quot;CN=Oliver Salzburg,OU=...&quot; unter dem Active Directory-Benutzer &quot;Active Directory operation failed on server.something.de. This error is not retriable. Additional information: Zugriff verweigert.
Active directory response: 00000005: SecErr: DSID-031521D0, problem 4003 (INSUFF_ACCESS_RIGHTS), data 0
&quot;.
Stellen Sie sicher, dass der Benutzer über geerbte Berechtigungen verfügt, die 'domain\Exchange Servers' erteilt wurden, um für Objekte vom Typ &quot;msExchangeActiveSyncDevices&quot; die Befehle 'Inhalte auflisten', 'Untergeordnetes Objekt erstellen' und 'Untergeordnetes Objekt löschen' auszuführen, und dass der Benutzer über keine verweigerten Berechtigungen verfügt, die diese Vorgänge blockieren.
Details:%3

English Version

Exchange ActiveSync doesn't have sufficient permissions to create the &quot;CN=,OU=,DC=thenet,DC=gen,DC=nz&quot; container under Active Directory user &quot;Active Directory operation failed on .thenet.gen.nz. This error is not retriable. Additional information: Access is denied.
Active directory response: 00000005: SecErr: DSID-031521D0, problem 4003 (INSUFF_ACCESS_RIGHTS), data 0
&quot;.
Make sure the user has inherited permission granted to domain\Exchange Servers to allow List, Create child, Delete child of object type &quot;msExchangeActiveSyncDevices&quot; and doesn't have any deny permissions that block such operations.

It boils down to a permissions issue for the Exchange server. It isn't allowed to change the ActiveSync settings in the Active Directory.
To resolve this, follow these steps:

Open Active Directory Users and Computers.
Click View and then check Advanced Features.
Navigate to the user that is causing the issue (the location is noted in the event log entry) and open the Properties for the user.
Go to the Security tab and click Advanced.
Check the checkbox Include inheritable permissions and click OK.