Have you tried chunking up the input side?

open (LOG, $file);
binmode LOG;
$linelen = 1024*1024;
while(!eof(LOG))
  {
    my($buf);
    $len = sysread LOG,$buf,$linelen;
    syswrite OUT,$buf,$len if($len);
  }
close(LOG);
[download]

The above is a chunk of code that worked for me, I assume that using file handles won't mess it up.

Update:Fixed the confusion between LOG (from the question) and IN (from my previous experience) (thanks bart)