Your CGI script loops as long as the socket is open:

    while ( $line = <$sock> ) {
        push @output, $line;
    }
    print $sock "BYE\n";
[download]

Your server doesn't close the connection until it gets a "BYE" from the client, but the client doesn't send a "BYE" until the server closes the connection. An easy solution would be to add a numeric or some other response from the server that marks the end of a command's output:

# In the server script
sub process {
   ...
           print $new_sock <<EOF;
OK
$output
123 End of output
EOF
}

# In the CGI script
sub execute
{
    while ( ($line = <$sock>) !~ /^123/ ) {
        push @output, $line;
    }
    print $sock "BYE\n";
}
[download]

-Matt