NTLM Authentication in the Outlook Anywhere

I use Exchange Server 2007 sp1 RollUp 6 installed on Windows Server 2008. I need to use Outlook Anywhere from non-domain computers. I test Outlook Anywhere with Basic and NTLM Authentication and all works fine. But when I use NTLM authentucation, Outlook promt user credential every time when it start, even "remember password" was checked. The login and password are remembered in the network password of user, but Outlook prompt password again and again, when it starts. Exchange published by 443 port directly (without any listeners)!

When I connect by VPN, and use TCP/IP connection to the server, Outlook remeber password withoun any problems, and did not ask password again.

get-OutlookAnywhere:

ServerName                 : SRVEXCH2
SSLOffloading              : False
ExternalHostname           : mail.my_domain.ru
ClientAuthenticationMethod : Ntlm
IISAuthenticationMethods   : {Ntlm}
MetabasePath               : IIS://srvexch2.net.local/W3SVC/1/ROOT/Rpc
Path                       : C:\Windows\System32\RpcProxy
Server                     : SRVEXCH2
AdminDisplayName           :
ExchangeVersion            : 0.1 (8.0.535.0)
Name                       : srvexch2
DistinguishedName          : CN=srvexch2,CN=HTTP,CN=Protocols,CN=SRVEXCH2,CN=Servers,CN=Exchange Administrative Group (
                             FYDIBOHF23SPDLT),CN=Administrative Groups,CN=First Organization,CN=Microsoft Exchange,CN=S
                             ervices,CN=Configuration,DC=net,DC=local
Identity                   : SRVEXCH2\srvexch2
Guid                       : 2c24f11b-852c-4948-b236-3f37d071d500
ObjectCategory             : net.local/Configuration/Schema/ms-Exch-Rpc-Http-Virtual-Directory
ObjectClass                : {top, msExchVirtualDirectory, msExchRpcHttpVirtualDirectory}
WhenChanged                : 18.02.2009 14:17:55
WhenCreated                : 17.02.2009 14:53:36
OriginatingServer          : dc1.net.local
IsValid                    : True


I have tried this cases, but they have not helped for this issue:
1) Disable kernel mode authentication with this command: %systemroot%\system32\inetsrv\AppCmd.exe set config /section:system.webServer/security/authentication/windowsAuthentication /useKernelMode:false, I  also have unchecked Kernel mode authentication in the properties of Windows Authentication for Default Web site, \Rpc and \Autodiscovery virtual directories.
2) Modify this registry key: HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Lsa lmcompatibilitylevel=3 and 2.
3) Set NTLM instead of Kerberos on the security tab in the properties of Outlook.
4) Install domain controller and global catalog roles on the Exchange Server.

Somebody have any solution for this issue? May be Outlook Anywhere and NTLM do not work at all?