Support

Most probably there is a problem with the FTP credentials and/or the directory. Make sure that these are correct by using the Test Connection button in the configuration page. For example, maybe your password changed in the meantime?

Do note that using the SSL option forces Akeeba Backup to try to use FTPS (FTP over implicit SSL) not SFTP (file transfers over the SSH protocol). FTPS and SFTP are completely different and incompatible protocols. That said, there is the issue of Active vs. Passive connections. Akeeba Backup only supports passive FTP. If your server doesn't work with Passive FTP over SSL, Akeeba Backup will indeed connect but it will not be able to transfer files to the server. The DynDNS should not be a factor, as long as the server's IP doesn't change in-between subsequent connections. If this happens, it's possible that the upstream DNS servers do not have the chance to "catch up" with the change, which won't allow the domain name to resolve to a valid IP and the connection will ultimately fail.

AFAIK the FTPS port is not 21. Normally it is port 990, but you'd better consult the documentation of the FTP server. It is very possible that a self-signed certificate would cause connection failure. AFAIK, PHP is using OpenSSL to route its SSL requests. By default, OpenSSL requires peer certificate validation (otherwise what's the point of having an SSL/TLS connection?). Apart from adding a self-signed certificate to the web server's certificate store, I don't know of any other way to convince PHP to not do certificate validation. Even if I did, I would probably refrain from putting it in the code, since the lack of signature validation doesn't protect you from man-in-the-middle attacks and defies the whole concept of the secure connection.

If you are security-minded, I will be including a new archive format in Akeeba Backup Pro 3.1, the JPS format. It is essentially a derivative of the JPA format which encrypts the file headers and file data with AES-128 encryption. This would allow you to safely transfer your backup archives over an unencrypted connection, as their contents would be useless to an eavesdropper who doesn't know your secret key.

Akeeba Backup - actually, PHP's FTP implementation - can only use FTP over implicit SSL. It cannot use FTP over explicit SSL. I think that the problem is that your server only supports FTP over explicit SSL. Unless PHP starts supporting something like that (or I finish writing a wrapper around cURL for Akeeba Backup 3.2) this won't work. That said, you can easily change the FTP port in Akeeba Backup's configuration, but I guess that your real question was "how can I use explicit SSL on port 21", right?