By default FileZilla is configured to transfer 5+ files at a time, which means that each time when you make a transfer, the application will initiate 5+ simultaneous connections to the server.
If you are hosted on a shared server and trying to transfer many files, the server firewall may block your IP address due to excessive number of simultaneous connections from one and the same address.
There is an easy way to reduce the number of simultaneous connections and transfers in FileZilla.
To reduce the number of simultaneous transfers, open the application -> Edit -> Settings -> Transfers. There you will see a field called Maximum simultaneous transfers - change the value to 1 and click on OK to save the changes.
To reduce the number of simultaneous connections, open the application -> File -> Site Manager -> select your site -> go to Transfer Settings tab -> check the box next to Limit number of simultaneous connections and set Maximum number of connections to 1. Click OK to save the changes.