If you have issues with sending SMTP messages from your wordpress host and have already checked the basics (username, password, firewall, ports, etc.) try to disable IPv6 on your server.
To do this add these lines below to the bottom of /etc/sysctl.conf
net.ipv6.conf.all.disable_ipv6 = 1
net.ipv6.conf.default.disable_ipv6 = 1
net.ipv6.conf.lo.disable_ipv6 = 1
Then run sudo sysctl -p or reboot the server. Enjoy!