Well, I "apparently" just found the answer. It seems a little while back, and I don't know when, they did something with their site that doesn't allow for the iPhone to receive push while you are still logged on. Another words, don't just leave the site while you are still logged on, but log off first.
I don't think they did this on purpose, but this has obviously happened.
I just tried this, and then sent an email from my other pop account to my Yahoo account, and received it on my phone a few seconds after I pushed send.
Really!