Here's a way to do it by subclassing HTML::Parser. Even though it is not well documented, I like the fine-grained control this technique allows. 
use strict;
use warnings;

my $html = q|
<h1>blah</h1>
<p>blah<p>
<h2>blah</h2>
<p>blah</p>
<h3>blah</h3>
<p>blah</p>
<h2>blah blah blah</h2>
<p>blah</p>
<h1>blah</h1>
<h2>blah</h2>
<h2>blah</h2>|;

my $parser = Markdent_Parser->new();
$parser->parse($html);
$parser->eof;
print $parser->out;


package Markdent_Parser;
use parent qw(HTML::Parser);

sub start {
    my ($self,$tag,$attr,$attrseq,$text) = @_;
    if ($tag eq 'h1' and $self->{'in_h2'}) {
        $self->{'out'} .= "</div>\n\n";
        $self->{'in_h2'} = 0;
    }
    elsif ($tag eq 'h2') {
        if ($self->{'in_h2'}) {
            $self->{'out'} .= "</div>\n";
        }
        $self->{'out'} .= "\n<div>\n";
        $self->{'in_h2'} = 1;
    }
    $self->{'out'} .= $text;
}

sub text {
    my ($self,$text) = @_;
    $self->{'out'} .= $text;
}

sub end {
    my ($self,$tag,$text) = @_;
    $self->{'out'} .= $text;
}

sub out {
    my ($self) = @_;
    if ($self->{'in_h2'}) {
        $self->{'out'} .= "\n</div>";
    }
    return $self->{'out'};
}

1;

[download]
The output is as described by your algorithm rather than as shown by your example (I fixed the typo in your input also). 
<h1>blah</h1>
<p>blah<p>

<div>
<h2>blah</h2>
<p>blah</p>
<h3>blah</h3>
<p>blah</p>
</div>

<div>
<h2>blah blah blah</h2>
<p>blah</p>
</div>

<h1>blah</h1>

<div>
<h2>blah</h2>
</div>

<div>
<h2>blah</h2>
</div>

[download]

In reply to Re: Wrapping HTML "sections" with a div by tangent
in thread Wrapping HTML "sections" with a div by nysus

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.