I am unable to reproduce your findings. Here are the results with perl 5.20.3:

$ cat 980408.pl 
#!/usr/bin/perl -w
use strict;

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

sub process_record
{
   my $line;
   while ($line = <DATA>, $line !~ /^END/)
   {
      print "$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
$ ./980408.pl 
These are the first
set of lines
which are to be extracted

New line
And new 
Will be extracted?

These are the second
set of lines
which are to be extracted

$
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