Run first as perl program.pl -BUG_MODE=0 (kcott's version); then as perl program.pl -BUG_MODE=1 (your version) ...

#!/usr/local/bin/perl -s

use warnings; use strict;

our $BUG_MODE;

printf "** Running in bug mode: %s **\n\n" , map uc( $_ ) , $BUG_MODE 
+? 'yes' : 'no';

my $re = qr{ \A \s+ ( \d+ ) }x;
my $high = 0;
my @lines;

my $filtered;
my $in_fh = \*DATA or die qq[Cannot open DATA: $!];
open (my $out_fh, '>' , \$filtered ) or die qq[Cannot open \$filtered 
+to write: $!];
while (<$in_fh>) {
    /$re/ or next;
    my $num = $1;
    next if $num < $high;

    if ( $num > $high ) {
      $high = $num;
      @lines = ();
    }
    push @lines , $_;
    $BUG_MODE
      and print $out_fh @lines;
}
close ($in_fh);

print "Highest number: $high\n";

$BUG_MODE
  or print $out_fh @lines;

close ($out_fh);

printf "Filtered output ...\n%s\n" , $filtered ;

__DATA__
High fanout nets in the post compile netlist:
    Fanout  Type          Name
    --------------------------
    2       INT_NET       Net   : c_c
                          Driver: c_pad
    2       INT_NET       Net   : b_c
                          Driver: b_pad
    2       INT_NET       Net   : a_c
                          Driver: a_pad
    1       INT_NET       Net   : sum_c
                          Driver: sum_1_SUM0_0
    1       INT_NET       Net   : N_5
                          Driver: sum_1_CO0_i
[download]

#  Output.
perl x.pl -BUG_MODE=0 ;  perl x.pl -BUG_MODE=1 ;
** Running in bug mode: NO **

Highest number: 2
Filtered output ...
    2       INT_NET       Net   : c_c
    2       INT_NET       Net   : b_c
    2       INT_NET       Net   : a_c

** Running in bug mode: YES **

Highest number: 2
Filtered output ...
    2       INT_NET       Net   : c_c
    2       INT_NET       Net   : c_c
    2       INT_NET       Net   : b_c
    2       INT_NET       Net   : c_c
    2       INT_NET       Net   : b_c
    2       INT_NET       Net   : a_c
[download]