I would use a parser for that instead. Here's some code to get you started should you choose this path:

use strict;
use warnings;
use Data::Dumper;
use HTML::TokeParser::Simple;

my $p = HTML::TokeParser::Simple->new( *DATA );
my $count = 0;
my @array;
while ( my $token = $p->get_token ) {
    next unless $token->is_start_tag('li');
    next unless ++$count > 3;

    while ( $token = $p->get_token ) {
        last if $token->is_end_tag('li');
        my $text = $token->as_is;
        $text =~ s/^\s*//;
        $text =~ s/\s*$//;
        push @array, $text unless $token->is_tag('br');
    }
    last;
}

print Dumper \@array;


__DATA__
<ul>
<li><strong>site_user</strong></li>
<ul>
<li>user1</li>
</ul>
<li><strong>compare_hidden</strong></li>
<ul>
<li>average_speed_answer  25 60 30 60 ^M<br />
 calls_waiting  300 500 300 500 ^M<br />
 many more rows here
 post_ivr_calls_handled Wisconsin 50 100 50 100 ^M<br />
 post_ivr_calls_handled Wyoming 50 100 50 100 ^M<br />
</li>
<li><strong>calls_waiting_good_high</strong></li>
<ul>
<li>300</li>
</ul>
<li><strong>calls_waiting_warning_low</strong></li>
<ul>
[download]

L-LL-L--L-LL-L--L-LL-L--
-R--R-RR-R--R-RR-R--R-RR
B--B--B--B--B--B--B--B--
H---H---H---H---H---H---
(the triplet paradiddle with high-hat)