Hard to say for sure without seeing the complete FTP sessions, but if I had to guess, the command connection in TIdFTP is likely being dropped part-way through the transfer, which would explain why the final response is not being received, and also why sending a QUIT request after the transfer timeout is causing a RST packet. Are you performing these transfers through a router/proxy/firewall, by chance? If so, they tend to drop idle connections after a few minutes, and thus are likely dropping the command connection during a large transfer since the command connection is sitting idle while the transfer is in progress. TIdFTP has a NATKeepAlive property to help avoid that issue, try enabling and configuring it as needed.
You should filter the logs to isolate just the FTP command connections before saving them. You don't need 500Mb to show a handful of packets.