iCloud SMTP timeout - what to do?

I am running OS X El Capitan 10.11.4 on Retina MacBoook Pro. I tried to send an e-mail from my iCloud account, but Mail says that there's a timeout when trying to connect to iCloud SMTP. Connection doctor is also trying to reach iCloud SMTP server, without any success (there is no red button, just permanently tries to reach out to the server). Incoming connection works properly (iCloud IMAP).

Tried to remove and reset iCloud account, but it did not get me to a solution, either. Do you have any suggestions how to fix this issue?