In order to reproduce your symptoms, if one of the START tokens doesn't start in column 1 (right at the beginning of the line), then then it wouldn't be recognized and that record would be skipped.

I made some slight changes to allow for START and END not being at the beginning of the line. Also, I eliminated the use of the "comma operator" in the sub's while statement in favor of an "and" statement. This should handle the case of a malformed record missing an "END" at the end of the DATA a bit better.

Your DATA as posted does indeed work as hippo demonstrates. This code should work on any Perl >= 5.6 - nothing "fancy" about it.

This is a very exacting business and when making a bug report, please post exactly the DATA that causes the problem, verbatim.

#!/usr/bin/perl -w
use strict;

while (<DATA>)
{
    process_record() if /^\s*START/;
}

sub process_record
{
   my $line;
   while (defined ($line = <DATA>) and $line !~ /^\s*END/)
   {
      print "$line"
   }
   print "\n";  #a printout spacer for next record
}

__DATA__

XXXX
YYYY
START
These are the first
set of lines
which are to be extracted
END
   START
New line
And new 
Will be extracted?
END
XXX
ZZZ
YYY
START
These are the second
set of lines
which are to be extracted
END
aasds
tteret
tertetr
[download]

As a comment, this malformed "START" record problem applies to all of the code in this thread. This is not unique to my code. "  START" vs "START" is my best guess as what you did wrong in your DATA.

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