Thanks for the replies.
The system is not using tcpwrappers, and it's also not a DNS issue. The client PC does have a reverse DNS entry. A tcpdump packet capture on the server shows the initial connection from the client followed by a bunch of DNS traffic, all within the same second. Then nothing happens for exactly 5 seconds, then the server sends data back to the client.
Just to be extra sure, I added an entry for it in /etc/hosts so DNS wouldn't even be needed. Still made no difference.
Thanks,
Dave