I think I figured out my problem. Perhaps this might help others. Installed this plugin: WP-Mail-SMTP and configured it. Required for sending webmail on many servers, like godaddy.
I am having a similar problem, but not exactly the same. It works for a while and then stops working, usually after I make a change. This has happened at least 4 or 5 times over the past month. I clear the cache and try on several different browsers, but get no emails. It starts to work after someone else tries it on their computer. Thought it might be a caching issue, but I keep cleaning the cache.