I've had other email issues with UA (recently talked with a couple of agents, both of whom said they sent an email, but it never arrived each time).
With the "Add Email Address and Request Receipt", I've sometimes made multiple requests in a row. I've found that when I did that, only the most recent one arrives. So I submit one request, wait for it to arrive, and then I make the request for another one if I need to. Given the responses on this thread, it sounds UA needs a major overhaul of their email system. (But I'm sure many of us would prioritize other UA IT issues first!)