It's not a failed to connect issue, despite being given that error.
Yes, you are right. I made an incorrect assumption not knowing you also upgraded WordPress.
The code that connects is just broken with this version. Also, I'm not the only one having problems. 5/7 people agree that it is broken.
Except this plugin doesn't contain the connecting code. That would be the PHPMailer library shipped with WordPress.
So you upgraded WordPress and bricked the blog. I've heard reports of connection problems with the newer PHPMailer.
In fact, to get around this PHPMailer problem, this other plugin silently disabled part of SSL altogether. Incredible. 😳
I switched to a different plugin and it works just fine.
Which one?