On all PHP Suites there is a limit of 8 simultaneous connections per user. Some FTP programs can create multiple connections to optimize speed, thus reaching the limit of 8 simultaneous connections relatively easily.
This is especially a problem with the programs CuteFTP and Filezilla.
If too many connections are achieved, we simply recommend waiting for the connections to close automatically and possibly. then set the selected FTP program to use fewer, or just one, simultaneous connections.
There is no speed limit on the FTP transfer. It is possible to switch to "Active transfer mode" in one's FTP program can provide an increased speed, although an increase in the opposite (passive transfer mode) is also possible. It is very dependent on one's firewall and such.