Without really knowing how you have implemented your server, I can give you the following advice if you are doing non-blocking I/O with the help of IO::Select or IO::Poll:

After getting a read-event on the socket, you'll go to do your sysread, and you'll get back 0 bytes. That means the client closed the socket. The following code snippet illustrates:

my $bytes_read = $socket->sysread($buf, $max_read_len);

if (not defined $bytes_read)
{
    print "ack!  error on the socket\n";
}
elsif ($bytes_read == 0)
{
    print "the socket was closed\n";
}
else
{
    print "woo hoo!  I read $bytes_read bytes from the socket...\n";
}
[download]

You might want to look at this node for more info:
Detecting a closed socket

HTH