Hello!

I have MS Exchange Server 2013 (Version 15.0 Build 847.32), it's single server with CAS and Mailbox roles.

MS Outlook(2013, 2010) for MS Windows work absolutely normally.

But MS Outlook(i tried 2011 and 2015 versions with last updates) for Mac OS (10.10) have a problem, this problem - lost connection with exchange server after some(random) time normally working and show me window of username and password request. 

If i input correctly username and password, it's ignored and windows show me again.
This problem is solved only by restarting Outlook.

Into Outlook log i see that:

2015-04-01 12:57:54.829,0xFFFFFFFF,Outlook Exchange Web Services,Warning,CExchangeNotificationMgr::CheckSubscription exception ErrorCode:-128 Error:

Into a IIS log (C:\inetpub\logs\LogFiles\W3SVC1) i see that:

2015-04-01 12:57:08 37.18.71.25 POST /EWS/Exchange.asmx &CorrelationID <empty>;&cafeReqId=17930f87-99a8-4447-9045-bb7a3f6a2553; 443 - 213.33.240.26 Mac+OS+X/10.10.2+(14C1514);+ExchangeWebServices/5.0+(213);+Mail/8.2+(2070.6) - 401 0 0 9

P.S. I tried find solution for this problem and turn off Digest Authorisation in IIS for EWS, but its not solve my promlem.

Hi,

According to your description, I understand that Outlook for mac always ask password with Exchange account, and restart Outlook is a temporary solution.
If I misunderstand your concern, please do not hesitate to let me know.

I want to double confirm whether all account with Outlook for mac client experience this question, or just some individual user.
First, please install latest update for Outlook and Exchange server.

Second, please run below command to double check the authentication:
Get-WebServicesVirtualDirectory | FL Identity,*Auth*

Also, do you deploy LB in your environment?
Please pay attention to below article about How to Configure SSL Offloading in Exchange 2010:
http://social.technet.microsoft.com/wiki/contents/articles/1267.how-to-configure-ssl-offloading-in-exchange-2010.aspx#Configuring_SSL_Offloading_for_Exchange_Web_Services_EWS

I find an similar thread about your question, for your reference:
https://social.technet.microsoft.com/Forums/exchange/en-US/1701bb51-7ecf-42e6-8589-bd1e6c0f77c1/outlook-2011-mac-and-exchange-2010-ews
v-betas solution: This is to update, that issue got resolved after changing the persistence settings for EWS from cookie based to IP based in Hardware Load Balancer.

Thanks