Just for fun, here's a solution that doesn't keep blocks of text in memory, and therefor may work for larger files.

Besides, how often does one get to use unshift, and set $/ to a reference :)

Notice also that you can seek around in DATA.

#!/usr/bin/perl

# https://perlmonks.org/?node_id=1216436

use strict;
use warnings;

my @sections;
while( <DATA> )
  {
  if( /^Title/ )
    {
    unshift @sections, [ tell(DATA) - length, length ];
    }
  elsif( @sections )
    {
    $sections[0][1] += length;
    }
  }

for ( @sections )
  {
  seek DATA, $_->[0], 0 or die;
  local $/ = \$_->[1];
  print scalar <DATA>;
  }

__DATA__
Title 1
Line of text A
Line of text B
Title 2
Line of text C
Title 3
Title 4
Line of text D
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