These steps should help fix or avoid the 421 Too many connections error.
1) Login to your cPanel
2) Click the FTP Session Control button in the Files section.
3) You will then see a list of all your current FTP connections. Click the red X in the Disconnect column.
4) You will then see a message similar to this "Are you sure you want to disconnect FTP user?." Click the Disconnect button to proceed.
You are finished when you see a message like this:"The FTP session with PID xxxxx was terminated.
Limiting Simultaneous Connections in FileZilla
1) Open FileZilla.
2) Access the Site Manager.
3) Click your site, then select the Transfer Settings tab.
4) Check the box for Limit number of simultaneous connections, and set the Maximum number of connections to 8.
5) Click the OK button. Now when you are using FileZilla, it will not allow you to go over your limitation of 8 simultaneous FTP connections.
Congratulations, now you know how to drop idle FTP connections in cPanel, and limit your FTP connections in FileZilla.