Try moving the client to a different machine. I used:

#! perl -w
use strict;
use IO::Socket;

my $host = $ARGV[0] ;
$|++ ;

my $con = IO::Socket::INET->new( "$host\:54321" )  or die "failed to c
+onnect: $!" ;

while (print $con "ping\n") { print "*" ; sleep 1 ; } ;

print "client ended: $!\n";
[download]

Set the two ends going. Disconnect the client machine from whatever network connects them. After a while, the client will give up. The server won't. (You can get the same effect by pulling the plug on the client machine, but I wouldn't recommend that.)

As far as the server is concerned, this is related to changing the your client to:

use strict ;
use IO::Socket ;
$|++ ;

my $con = IO::Socket::INET->new( 'localhost:54321' ) or die "failed to
+ connect: $!" ;

for (1..20) {
  print $con "ping\n" ; print "*" ; sleep 1 ;
} ;

print " client hanging" ;

while (1) { print "." ; sleep 60 ; } ;
[download]

except that when you finally get bored and terminate the client, the OS will close the client end of the connection and the server will get to hear about it.