Can't send email via iCloud account

Using the Mail application on my Macbook, I have my iCloud email account set up. It receives messages perfectly but seems to be unable (currently) to send emails. A check of the iCloud server status indicates no problems, and yet, every time I try to send emails, I get the following error:

"Cannot send message using the selected server iCloud (iCloud)

Connections to the server “p02-smtp.mail.me.com” on the default ports timed out.

Select a different outgoing mail server from the list below or click Try Later to leave the message in your Outbox until it can be sent.

Sending from: xxxxxxxx <xxxxxxxx@icloud.com>"

The option in the list below often (but not always) says: "iCloud (iCloud, Offline)".

I have tried manually setting up a new outgoing server as smtp.mail.me.com, using instructions found here http://support.apple.com/kb/TS4002 but to no avail.

Any useful ideas?