I'm just posting this as I did for all these threads for the same issue:
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...
But according to the nslookup command there are only the servers "p01, p02, p03, p04"... no p05 and p06 or p07 and p08 ...
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!!
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!