Beginning in July of 2015, I've been unable to send mail using the Mailgun SMTP server using Mac Mail. To add a Mailgun account, I go to Mail > Preferences and under Account Information > Outgoing Mail Server (SMTP)
I choose the Edit SMTP Server List option. I select the options shown in the images.
When I hit OK, the account description in the Outgoing Mail Server (SMTP) briefly changes so that the "(Offline)" suffix is removed, but then it is quickly added back and I can't send with that account.
As suggested by Mailgun at https://documentation.mailgun.com/quickstart-sending.html#send-via-smtp,
I tried sending with swaks and was successful, though I had to change the password provided by Mailgun's example.
Best Answer
Go to: Connection Doctor in the Windows menu item...
Then enable the log, or select show details to see if anything in the log helps you to see what the issue is...