The domain configuration done in Mailgun is in US region but the plugin configuration was set to Europe. That is the root cause.
We are using WP 4.9.8 with Mailgun plugin version 1.5.13.1
No other email management plugin.
Ok, found the issue. The MailGun Region configured in the WP plugin was wrong.
It would be great to have error message corresponding to the problem 🙂