And to comment on my own issue, this test script

use strict;
use warnings;
use IO::Socket::INET;

sub server {
    my $server = IO::Socket::INET->new( LocalPort => 12000,
                                        Proto     => 'tcp',
                                        ReuseAddr => 1,
                                        Listen => SOMAXCONN
    );

    die $! unless $server;

    while (my $sock = $server->accept) {
        print "Connected to $sock\n";
        print while <$sock>;
    }
}

sub client {
    my $sock = new IO::Socket::INET( PeerAddr => '127.0.0.1',
                                     PeerPort => 12000,
                                     Proto    => 'tcp',
                                     Blocking => 1
    );

    print $sock "yes\n";
    print $sock "no\n";
    print "sock is $sock\n";
}

fork || server();
fork || client();
fork || client();

sleep 100;
[download]

Works as expected: both "yes" and "no" are correctly outputted even though only one client is connected at a time.

There must be something in my code that's eating the additional lines of text.

Sigh. Thanks for letting me talk this out! :)