Internet Accounts not able to verify Exchange account

Two days ago, all of my OSX devices (an iMac and two Macbooks - three of them) suddenly stopped being able to connect to accounts set up on them. I had made no changes to the accounts on the server and no setting changes to the Macs. I opened Apple Mail on the iMac and was prompted for the Exchange password. I typed it in, clicked "OK" but was given the response, "unable to verify account name or password". The other two Macbooks started doing the same thing.

I am able to access the Exchange account via a web browser (which confirms that I am using the right e-mail/username and password). The same thing started happening on my iPad and iPhone. I was able to delete the accounts on the iPad and iPhone, re-add the account and all is now working there. The problem is when after deleting the Exchange account on the iMac and the Macbooks, I continue to get the message through Apple Menu/System Preferences/Internet Accounts/PlusSign/Exchange that it is "unable to verify account name or password" when I know that these are right.

All machines are running OSX High Sierra.

I have turned off iCloud keychain but that hasn't fixed it. Any other solutions?