Create a new Outlook Profile. Exit Outlook.
Go to the Control Panel and search for 'Mail ' - This should return: 'Mail (Microsoft Outlook 2013/2016) (32/64 bit)' - Click this and a new window will open called Mail Setup. In the Mail Setup - Outlook dialog box, click the Show Profiles button. On the General tab, click Add. In the Profile Name box, type a name (this can be anything) for the new profile, and then click OK. Click Next for Auto Account Set Up.
Outlook for Mac: Version 15.21.1 (160411) OS X: 10.11.4. Ever since some updates within the past month Outlook started asking for password every single time it started.
Be sure that the Always use this profile radio button is selected. Note: If you are performing these steps to create a 'new' profile because you are having problems with an 'old' profile, you will not remove the original profile as of yet. From the drop-down list, choose the new profile that you just created. You are now ready to open the new profile. Open Outlook normally. You should see the following message: ' Preparing Outlook for first use Retrieving mailbox settings.' .
Outlook should then open (In the lower right you will now see the words ' Connected to Microsoft Exchange') At this point you are done. However, Outlook is downloading a copy of your mail from the Exchange server. You will see it ' Updating.' Folders in the lower right. You should allow this process to complete. You may stop it. But then you won't have access to all your mail if you then Work Offline.
Follow-up: After 1 - 2 weeks, you can reopen the Mail control panel, click the Show Profiles button. On the General tab, select the original Profile and click Remove. Upgrading to the latest version can fix Outlook connection problems.