I have a shared web hosting account on a Windows Server at Godaddy, and use relay-hosting.secureserver.net with no authentication on port 25. This was the only configuration that I found to work on Godaddy because I use a an email account that is hosted on Godaddy. The FROM email configured on both WP-mail-SMTP and CF7 must be identical, and there can be no other SMTP mail configuration plug-in installed. This configuration worked fine for about a year, but then suddenly after upgrading from CF7 2.4.1 to CF7 2.4.3, everything stopped working, even though the test tool on WP-mail-SMTP still worked.
I tore my hair out trying to figure it out. I still have no explanation, and Godaddy support pretty much told me I was on my own because WordPress is not their product.
So after scouring countless forums, I found a link to a very old version of CF7 (1.9.5), so I decided to uninstall CF7 2.4.3 and install CF7 1.9.5. That didn’t appear to work, so I re-installed CF7 2.4.3 and to my pleasant surprise, CF7 worked again. I thought at first it was the act of uninstalling CF7 2.4.3 and reinstalling CF7 2.4.3 that did the trick, but after experimentation I found that it was actually the installation of CF7 1.9.5 prior to the re-installation of CF7 2.4.3 that did the trick. It made no sense, but I think there’s something about installing 1.9.5 that configured something on my WordPress installation that makes WP-mail-SMTP work again. Here is the link to CF7 1.9.5: http://www.idiotproofblogging.com/reports/contact-form-7.zip
Hopefully that will help some of you who had it working, then suddenly stopped for no reason after the upgrade. For me, just uninstalling and re-installing CF7 2.4.3 wasn't good enough. I had to install and uninstall CF7 1.9.5 first. Weird, but works for me.