I got exactly the same error on Apple mail in my macbook, and i solved it by deleting the login items for mobile account in my keychain. i guess iCloud was messed with the passwords saved in the keychain.
Go to appleid.apple.com and change your primary email address to something else. It doesn't matter if the primary email address doesn't match your @me.com address, iCloud will still work by using your @me.com address.
If you can't delete it from that site, try logging in via iTunes and editing your account address that way.
Ok I think this problem here is Apple... It's a DNS problem. You get this problem depending on what smtp server you are registered on.
I always get the message that "p06-smtp.mail.me.com" failed...
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But according to the nslookup command there are only the servers "p01, p02, p03, p04"... no p05 and p06 or p07 and p08 ...
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What I did to get it to work (only considered as workaround):
first I tried to add a second SMTP server with the address "smtp.mail.me.com", it seemed that the mail went through... but never arrived... then I configured "p01-smtp.mail.me.com" as second server and it worked!!
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What is the problem with this workaround?
When you change the password! As it doesn't accept the Apple Token you must configure your Apple ID credentials manually... however when you change them, you have also to change the manually configured second SMTP server!
This is inexcusable as BETA ran for months to hash out all these issues. Planing for capacity did not take place... How embarrassing after all the talk of mobile.me shortcomings...
As noted above, if you remove all keychain entries related to me.com, mail appears to successfully connect however it is painfully slow...
Wow - that seems to have worked.
I'll get back to this thread should it stop working - but for now, thanks!! Any idea as to why this is happening?
Ok boys and girls I think I have found the fix and it is working for me so far so I wanted to share....
Mail > Preferences> Accounts> iCloud> Account Information Tab> Bottom of screen TLS certificate> click on the arrow and place the number in the box versus none> Advanced Tab> Bottom of the screen uncheck use Idle command if server supports it..... Save....
Mine is working great so far hope you have the same experience...