Had a bit of fun with this. I'm sure there is a much shorter and better way, but alas, it is what it is :) Using your data:

#!/usr/bin/perl

use warnings;
use strict;

my @hold;
my @data;

while ( my $line = <DATA> ){
    
    chomp $line;

    if ( $line =~ /NIL$/ || $line !~ /\w+/ ){

        if ( scalar @hold > 1 ){
            push @data, [ @hold ]; 
        }

        undef @hold;
        next;
    }
    push @hold, $line;
}

for my $block ( @data ){
    for my $entry ( @{ $block } ){
        print "$entry\n";
    }
    print "\n";
}
[download]

EDIT: Fixed code so it would work with more than two consecutive lines.