update: Oops, I wasn't thinking either. My eval/alarm solution will not work because the connection is successfull and therefore it contains the exact same issue as the OP. Sorry. *sigh*

In lieu of the completely refactored parent node, here is the refactored answer :)

When you set a socket to listen() via IO::Socket::INET, the port will come up as in-use and will queue up successive connection requests. Since your first client that connects is in an infinite loop, the second client to connect is simply waiting for the first client to close the connection to the server.

The easiest way to fix such a problem is to set a timeout via a signal handler. Such an example is provided here (see the last paragraph of screen 7 of `perldoc perlipc` on a 24-row terminal for an explanation of the $SIG{ALRM} and alarm()):

#!/usr/bin/perl
# c.pl
use strict;
use warnings;
use IO::Socket;
use less 'java';        #;-)
my $b_address = '127.0.0.1';    #IP of box A
my $b_port = '8888';        #Port number guipartner set to on A
my $eol = "\015\012";   #sets end of line chracters for socket transmi
+ssions
my $skipC = 0;

my $socketC;
eval {
    # set the signal handler. we die when the signal hits us
    local $SIG{ALRM} = sub { die("timeout\n") };
    alarm(5); # number of seconds for timeout

    $socketC = new IO::Socket::INET (
        PeerAddr => $b_address,
        PeerPort => $b_port,
        Proto => 'tcp',
    );
    alarm(0); # cancel the alarm signal
};

# we got the alarm signal, so we timed out
if ($@ eq "timeout\n") {
    print "socket not available\n";
    exit;
}

# some other unexpected error
elsif ($@) {
    die($@);
}

local $/=$eol;          #set default EOL to $eol so chomp works
while (!$skipC) {
    print $socketC "c.pl sends \$skipC=$skipC", $eol;
    print "message sent\n";
    sleep 2;
}
print "socket not available\n";
close $socketC;
[download]

Also, you can modify your server code (b.pl) so that you're not recreating the socket for each connection. You can instead move the socket creation outside of the infinite loop and loop on accept():

#!/usr/bin/perl
# b.pl
use strict;
use warnings;
use IO::Socket;
use less 'java';    #;-)
my $eol = "\015\012";    #sets end of line chracters for socket transm
+issions

my $sock = new IO::Socket::INET (
    LocalPort => '8888',
    Proto => 'tcp',
    Listen => 1,
    ) or die "Could not create socket: $!\n";

while ( my $newsock = $sock->accept() ){        #continuous loop: wait
+ for socket connections until end of time
    while (my $incoming = <$newsock>){
        local $/=$eol;            #set default EOL to $eol so chomp wo
+rks
        chomp($incoming);
        print "received: $incoming\n";
    }
    close $newsock;
    close $sock;
}
[download]