Helpdesk of seznam.cz told me: "Hello, we had problems with new IMAP implementation, however in yesterday afternoon, new version of IMAP was implemented and in new messages, attachments should be downloaded correctly (unfortunately only in messages delivered after new version was implemented, not the old ones) could you test it right now on some today´s e-mail message? If problem is still here, please leave message in inbox and send me exact time of download attempt"
I tried sending a new message with attachment today and it worked! :-)