Can't send iCloud mail through mail app in OSX

I can't send mail through the mail app in OSX for my iCloud account.

I tried:

1. Having the account automatically setup when creating my iCloud account. This didn't work, as it gave me a message stating that the connection to the servier timed out when it tried to contact it on the default ports.

2. Disabling / reenabling mail in iCloud preferences . (Made no difference).

3. Edited the SMTP server list, and specified a different server (p01-smtp.mail.me.com instead of p08-smtp.mail.me.com). This worked for a matter of a few hours. Now it no longer works and informs me that my password has been rejected.

This seems ridiculous. I just created my me.com account. Neither does the automatic setup work, nor do the iCloud server settings on apple's knowledgebase article work. How am I supposed to use my iCloud mail then?