Nearly all FTP servers are configured with site to site transfers disabled by default.
This is a setting that must always be changed in order to allow site to site transfers.
In most cases you will need root access on the machine to re-configure the FTP server to allow site to site transfers, as this requires editing the FTP server configuration file.
ProFTPD requires setting the config option AllowForeignAddress = on in the proftpd.conf
http://www.proftpd.org/docs/howto/FXP.html
PureFTPD requires using the command line switch --allowuserfxp
vsFTPD requires setting the config option pasv_promiscuous = yes in the vsftpd.conf
http://vsftpd.beasts.org/vsftpd_conf.html
FlashFXP also supports indirect site to site transfers where the transfer is downloaded to your local machine and then uploaded to the destination server, this mode is intended for people who want the ease of site to site transfers but are unable to re-configure their servers to allow direct site to site transfers.
To configure FlashFXP to use indirect site to site transfers from within FlashFXP > Site Manager > Select your site > Transfer Tab, now Change the site to site method to "indirect (protocol independent)" and click the Apply button. Now try your transfer again, this time it will be performed indirectly and should transfer without any problems.