I have many Outlook clients (2007 and 2010) with the password prompt at every startup.
I saw that Outlook receives email also without login, and so I checked the connection status with outlook.exe /rcpdiag.
The connection status window shows two connection to OAB with the same server name and the same proxy. In working clients (where password is not prompted) I checked that Outlook connects to OAB once.
Can be useful to say that my Exchange 2013 server comes from an hard migration from Exchange 2010 and I think some clients are still looking for the old OAB, however the connection status shows the correct server name. Moreover I can not understand why some clients had no problems.
Thank you for you help.