I am experiencing the exact same scenario. Everything you describe is my exact situation. I’ve used this plugin for more than a year with no issues but it’s been really problematic over the last few months.
I just found an 8 year old discussion board and the client had the same problem. They were told to use the following SMTP Host: relay-hosting.secureserver.net and it worked!! I spoke to 2 people at godaddy and they told me to use smtpout.secureserver.net That does not work. I think this is resolved now. Thank you!