If you use FileZilla software: To limit the number of connections of an EXISTING configured connection, you need to go to the Site Manager, click on the "transfer settings" tab. Check the "limit number of simultaneous connections" and then write 4.
If You do not use a configured connection (No site manager), then simply go to Edit -> Settings -> Transfers then for "Maximum simultaneous transfers" put "4". Make sure that there are no errors during transfer.
All other FTP clients should also have an option to limit maximum simultaneous transfers, so set it as low a possible and you will never get this error again.
To speed up the connection, it is recommended to archive Your data and then upload it. After that, you may use cPanel's "File Manager" to extract the archive to any folder You like.