The problem usually appears due to firewall on your server that blocks connections from website builder server on port 21.

For Cloud brand:

Allow connections from Site.pro IPs on your server on ports 21, 80 and all ports that you have configured for passive FTP connections.
Here is the example command to whitelist specific IP on the server:
iptables -I INPUT 1 -p tcp -s 18.196.241.217 -j ACCEPT
Note: the command can vary depending on firewall service you use on your server.

For everyone:

1. You may not have FTP service running on your hosting server. This can be checked by running service status:
service proftpd status
service pure-ftpd status
If none of them return active (green) status, then you need to enable the one which you have on your server installed.
Note: On cPanel server, you can enable FTP service per WHM "FTP Server Selection" menu.

2. You may use a custom FTP port (not default 21). If so, you need to set up it on Site.pro. To do this, take the following steps:

1. go to licenses page;
2. click button "Manage" to open the brand;
3. switch to section "Configuration";
4. scroll down and find the setting "Custom FTP port";
5. enter your custom port and click button "Apply" in the bottom of the dialog;
6. open website builder again from your hosting panel and check whether publication started working.