After reading through some forums, it sounded like it was a problem with being hosted by Go Daddy and possibly a missing plug-in.
So, I made sure I had the most recent plugin for Subscribe 2 V. 7.1 (which I did). I downloaded the plug-in for WP-Mail-SMTP so that my messages would go out using SMTP instead of mail. Then, I called Go-Daddy and asked them to run a diagnostic to see what was wrong and explained that a forum indicated habitual issues with Subscribe 2 for Go-Daddy users.
They ran the diagnostic and said everything was up and running properly.
I sent several test posts and informed my readers in the test post that I was having some technical issues. I subscribed via the Subscribe 2 button on my site using an alternate email to test the test posts. They all came through. However, there was a delay. I would say the delay was by nearly an hour. This resulted in my initial thought that it was not working- so I sent out multiple test posts.
I would wait at least an hour or two before sending additional tests.
The plugin has worked for me since I took these actions.