I set up a socket 'manually', just after the $server undef, and before restart:

.
.
$log->warning('Server has stopped - we need to restart!');
$server = undef;

use IO::Socket::INET;
use IO::String;

my $listen = IO::Socket::INET->new(
    Listen    => 5,
    LocalAddr => 'localhost',
    LocalPort => 12345,
    Proto     => 'tcp',
    ReuseAddr => 1
);

while( 1 ){
  $log->warning( "listening....\n" );
  sleep 5;
}
&restart_daemon;
.
.
[download]

The client seems quite happy to connect to this newly created socket..

I am really baffled.