If the FileZilla uses multiple connections to download/upload the files and that is the reason your IP is getting blocked, Make sure you select passive connection under transfer settings of FileZilla , there is another workaround.
1. Open the Site Manager (File – Site Manager… or the first toolbar button)
2. Create an entry for that server, enter all details you know, the more precise, the better
3. Open the ‘Transfer Settings’ tab
4. Tick the ‘Limit number of simultaneous connections’ checkbox
5. Enter the desired limit into the ‘Maximum number of connections’ field
Now, if you connect using the Site Manager entry, connections will be limited.
If these tricks do not work then please use WS_FTP pro FTP client with passive mode as this client doesn’t create multiple connections while uploading or downloading files.