Good points. I'm not sure I totally agree. Shutdown(1) forces a close of half the socket. That's fine and inline with what I said. In order for this to happen, on the TCP level, a FIN must be sent to the other end. That end will answer back with an ACK of it's own, which completes the shutdown of HALF of the socket.
My next statement is a bit misleading I guess. You are correct that the other side does not have to initiate a shutdown of the other half of the socket right away. However, it's probably better to keep both halves of the socket open until you're done sending and receiving. This would allow multiple requests in a single session. That may not be required NOW, but experience has taught me that those who dictate what you need to code will oftimes ask for things you thought you'd never need.
But I guess it's moot, because the bottom line is the protocol is going to have to change, since the other end is apparently enterpreting the shutdown of half the socket as a hard close of the socket.
I'll admit to one thing... I've never actually used IO::socket, and am making some assumptions based on documentation I can find. If I'm way off, please tell me exactly how. I think I've got it right though.