Some FTP clients now days try to open a connection for every file you try to download or upload so when you grab and entire site with several hundred files and a different connection is opened for each of them the server will lock you out. It is a simple fix on the ftp client side jsut change the settings to the concurrent connections to a reasonable amount like 3 to 4 and the problem goes away.
Can I make the change on the server to stop it? Yes I can but if I do and you have 2 or 3 people on that server decided to open that many connections at once you entire server is going to stop responding while they are using up all the available connections and it is going to open a security hole on your server and open it up to ddos attacks that hackers can use to create buffer overflows and try and gain root privileges.
Right now the limit is set on the FTP to 50 connections from a single IP you are making more than that if you are being blocked so setting the concurrent limit in the FTP client stops the issue and does not compromise the server.
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you should configure your firewall to ignore ftp port or set maximum connection from single IP to 50 and in your firewall config it to block more than 60 connection so IT never block by firewall because the ftp server reject connection when use reached 50 connections.