Hey,
EXACTLY the same problem. Very serious - I'm not getting any emails now. My mail client pings that new email has arrived, but nothing in the inbox.
@pvonk: It's not a computer email client problem. I tested this on the iCloud webmail: The messages appear for a split second, then immediately disappear, not to be found anywhere, not in Junk, Trash, anywhere.
Fact is, I cannot use iCloud email anymore. Simply because I'm not getting any email!
EDIT: I found that a workaround is possible by setting up iCloud to forward all messages to another address. It seems the messages go through to the forward address, while still not appearing in the iCloud mailbox. So this is a way to preserve the incoming messages. Just have to make sure to let everyone know to stop using my iCloud address to send me mail in the future.
Message was edited by: estibot