Since the log files are sorted, there's no reason to have more than two handles open.

while (my $logfile = glob('access-????.log')) {
   open(my $logfile_fh, '<', $logfile)
      or die("Unable to open yearly logfile $logfile: $!\n");

   my ($year) = $logfile =~ /^access-(....)\.log$/;

   my $output_fh;
   my $month = -1;

   while (<$logfile_fh>) {
      # Extract month of log entry.
      my ($new_month) = /$year-(..)/;

      if ($new_month != $month) {
         $month = $new_month;
         my $output_file = sprintf('access-%04d-%02d.log', $year, $mon
+th);
         open($output_fh, '>', $output_file)
            or die("Unable to create monthly logfile $output_file: $!\
+n");
      }

      print $output_fh $_;
   }
}
[download]