You may experience getting too many connections from IP error when trying to access FTP and not able to connect to the FTP server. To rectify the error message, follow the instructions from this article.
1) Login to your cPanel.
2) Click on FTP Connections under Files panel.
3) You will see a list of your connections. Click on the button in the DISCONNECT column as long as the status of the connection states IDLE.
4) You might have to click on the DISCONNECT button several times to remove all of the connections.
Just make sure that you clear out all of the connections listed and then try logging again. I did just go in myself and clear the connections. The connections should clear out when you disconnect from FTP.
If you wish to change the maximum simultaneous transfers do follow the below order in your filezilla client.
[FileZilla -> Edit Menu -> Setings -> Transfers -> Maximum Simultaneous Transfers]