First, I commented out the exit. It "fixed" the problem, but I deemed the solution unacceptable. Behold my fancy debugger!

#!/usr/bin/perl

use strict;
use IO::Socket;
use constant MYPORT => 2000;

$|=1;  <-------

my $sock = '';
my $client = '';

$sock = IO::Socket::INET->new(LocalPort => MYPORT,
                              Type      => SOCK_STREAM,
                              Proto     => 'tcp',
                              Reuse     => 1,
                              Listen    => 10)
or die "trouble creating socket: $@\n";

$SIG{'CHLD'} = sub { 
print('!');  <-------
wait();
print('@');  <-------
$client->close();
print('#');  <-------
};
print "Accepting connections on Port ", MYPORT, "...\n";
while ($client = $sock->accept())
  {
  print "Accepted connection from ",
        $client->peerhost(), ":", $client->peerport(), "\n";

  if (fork() == 0)
    {
    while (<$client>)
      {
      chomp;
      print $client scalar(reverse($_)), "\n";
      }
    exit 1;
    }
  }

print('$');         <-------
print(0+$!, "$!");  <-------
[download]

When I noticed '!@#' was being printed, I added '$'. Then I checked why accept was returning by adding a print of $!.

Since I'm not sure what the cause is, I'm not sure if I consider it a bug. In any case, the behavious should be documented.