You can use $/ (see perlvar) and set it to a string to control what the diamond operator see's as a line ending. By setting this to 'head' and then 'tail' alternately, you can move through you large file in chunks, discarding the 1st, 3rd, 5th and printing the 2nd, 4th & 6th etc.

#! perl -slw
use strict;

open IN, '<', $ARGV[ 0 ] or die $!;

$/ = 'head';
 while( <IN> ) {
     local $/ = 'tail';
     print scalar <IN>;
 }
close IN;
__END__
P:\test>type junk.txt
The quick brown fox jumps over the lazy dog           0001
head The quick brown fox jumps over the lazy dog      0002
The quick brown fox jumps over the lazy dog           0003
The quick brown fox jumps over the lazy dog           0004
The quick brown fox jumps over the lazy dog           0005
tail The quick brown fox jumps over the lazy dog      0006
The quick brown fox jumps over the lazy dog           0007
The quick brown fox jumps over the lazy dog           0008
headThe quick brown fox jumps over the lazy dog       0009
The quick brown fox jumps over the lazy dog           0010
tail The quick brown fox jumps over the lazy dog      0011
The quick brown fox jumps over the lazy dog           0012

P:\test>235232 junk.txt
 The quick brown fox jumps over the lazy dog      0002
The quick brown fox jumps over the lazy dog           0003
The quick brown fox jumps over the lazy dog           0004
The quick brown fox jumps over the lazy dog           0005
tail
The quick brown fox jumps over the lazy dog           0009
The quick brown fox jumps over the lazy dog           0010
tail
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The caveat is that if the chunks you are discarding (between 'tail' and then next 'head' marker) are very large, they will consume large amounts of memory.

As implemented above, the 'head' marker is discarded, but the 'tail' marker is printed. Add or delete as neccessary.

This also assumes that by "including the lines the key words are on.", you do not mean that you want any text preceding the 'head' marker, if the head marker is in the middle of a line, nor anything after the 'tail' marker if it can appear in the middle of a line.