BestFTP Explorer | Shareware | Homepage | Screenshot
FmEdit no longer includes an FTP client, BestFTP Explorer is what I use and I highly recommend this, it only costs $10 although you can try before you buy, below are just a few of the many features this program has.

Integrated and Fmedit Explorer-style user interface 
BestFTP Explorer provides Site Book which makes your favorite site management easy using folder style, Local Explorer and Remote Explorer like FmEdit or Windows Explorer, Online Editor which can edit the remote file and Multi-threaded transfer manager called Carrier.

Auto-reconnecting 
BestFTP Explorer never send NOOP command not to be disconnected. But when you send FTP server command, if it finds disconnection at that time, it will try to reconnect to FTP server. So, it makes you think always connected.

FTP server to FTP server transfer directly not via local system 
When the server to server is transferring, BestFTP Explorer makes servers communicate directly not via local system. Using multi-connections to FTP server feature and copy/paste or drag/drop features, you can transfer FTP server to FTP server directly.