Mail from one of my iCloud accounts does not load in OS X Mail
I have this very weird problem. I have two iCloud email accounts, both of which were carried over from me.com. My first iCloud email account works perfectly, and always has. The second one is having problems ever since it was converted from me.com to iCloud.
I can access it with Safari or any other browser through http://www.icloud.com/. Absolutely no problem there.
The problem occurs when I try to access it with Apple Mail (Version 5.3, OS 10.7.5): Mail will load the mail headers and display them in the list of mails, but when I click on a certain mail in the list, Mail only shows "Loading" in the message window, but the message will not load, not ever after an hour of waiting.
Selecting "Rebuild" from the "Mailbox" menu makes the problem go away, but only for the present session. When I quit Mail and relaunch it, the problem is back.
I also tried deleting the mail account and adding it again, but the problem does not go away.
The truly weird thing is that the problem does not appear on all three Macs I'm working on. My Mac Pro at the office never had the problem at all, my MacBook Air had the problem for a while and then it suddenly went away, but my iMac has had the problem ever since my account was converted from me.com to iCloud.
Needless to say, the account configuration on all three machines is absolutely identical.
Any ideas?
iMac 3.2 GHz Intel Core i3, 4 MB RAM, 1TB HD, Mac OS X (10.7)