I'm having the same problem with my iCloud email account. It suddenly stopped receiving email (but can still send it). I started my own thread on the problem, and here's what I said:
"I have spent the past 2 days on the phone with Apple support (senior technical staff). My problem is that several days ago I stopped being able to receive email at my iCloud email address. I originally had a me.com email address, and received an iCloud alias when Apple switched over to iCloud. I've been using the iCloud address to both send and receive email for years. That all changed several days ago. Without warning, I could no longer receive email at my iCloud address. But I was still able to send email from the iCloud address. I can both send and receive from the me.com email address. I performed no software updates just prior to this happening, and the problem occurs on my iPhone, MacBook Air, and Mac Pro.
After a number of troubleshooting steps, the senior tech person told me that this was expected behavior. She asked the other senior tech people in the call center and they agreed with her. I think she and the other senior techs are wrong. Why would this problem appear suddenly after years of being able to fully use my iCloud email address? Why can my wife still send and receive email at her iCloud email address? And most importantly, what can I do to fix my problem?
She is going to forward my problem to the engineers, but she told me that I shouldn't be surprised if they came back with the same answer she did.
Thanks in advance for your help!"
Were you able to solve your problem, and if so, how?