I tried your script. The while loop just wouldn't work, so I abandoned it and tried it like this.

#!/usr/bin/perl -sl

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

my $socket = IO::Socket::INET->new(
             PeerAddr => '192.168.1.1',
             PeerPort => 'http(27109)',
             Proto    => 'tcp',
);
$socket->accept();
if($socket->connected) {
    print "This is a test";
}
else {
    print "Sorry! This is not what you wanted\n";
}
$socket->close();
sleep 3;
unless($socket->connected) {
    print "This test has closed";
}
[download]