Testing on non-CygWin (Activestate Win32), trying to replicate the possible test/binary condition. This (highly refactored) code, when reading and writing binary (raw), works perfectly. Changing the output mode back to Text reproduces the behaviour described in the OP.

use strict;
use warnings;

my $self   = { data => 'PM_618194_in.dat', process => 'patient' };
my $config = { blocksize => 550, startblock => 3 };
my $max_chunk_size = 1_000_000;

my $chunk_size = int( $max_chunk_size / $config->{blocksize} )
               *                        $config->{blocksize}  ;

open my $parent_fh, '<:raw', $self->{data}
  or die "Cannot open '$self->{data}' for incremental parsing: $!";

my $bytes_read = read $parent_fh, my $junk, $config->{startblock};
if ( $bytes_read != $config->{startblock} ) {
    warn "Tried to read $config->{startblock} bytes, ".
         "but got $bytes_read bytes!\n";
}

$/ = \$chunk_size; # Set <> for fixed blocksize reads.

my $file_num;
while ( <$parent_fh> ) {

    $file_num++;

    my $filename = sprintf 'tmp/%s%02d.dat',
                           $self->{process}, $file_num;

    open my $out_fh, '>:raw', $filename
#    open my $out_fh, '>', $filename
      or die "Cannot open '$filename' for incremental writing: $!";
    print $out_fh $_ or warn;
    close $out_fh    or warn;
}

close $parent_fh or warn;
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BTW, you can save yourself a good bit of code by factoring out the {startblock} read, and using $/, as I have above. Also, when your files are binary, it is *always* most correct to use binary mode, even when your OS (like Unix) does not care.