You are working with HTML (even XHTML!) so your best bet is to use one of the many parsing modules available.

HTML::Parser for example.

If you look at the source of the web-page you see that the latest update is within <kilauea_update>-tags, so all you have to do is extract the text between these tags.

use strict;
use HTML::Parser ();
use LWP::Simple;
my $url="http://volcano.wr.usgs.gov/hvostatus.php";

my $mypage=get($url);

# Create parser object
my $grab_text = 0;

my $p = HTML::Parser->new( api_version => 3,
                        start_h => [\&kilauea_update_tag_start, "tag"]
+,
                        end_h   => [\&kilauea_update_tag_end,   "tag"]
+,
                        text_h  => [\&textgrabber,              "dtext
+" ],
                      );

$p->parse($mypage);

sub kilauea_update_tag_start {
    my $tag = shift;
    return unless $tag eq 'kilauea_update';
    $grab_text = 1;
}

sub kilauea_update_tag_end {
    my $tag = shift;
    return unless $tag eq '/kilauea_update';
    $grab_text = 0;
}

sub textgrabber {
    my $text = shift;
    print $text if $grab_text and $text=~/Activity Summary for last 24
+ hours:/;
}
[download]

Of course you may wish to save the the text in a variable or file. That is left as an exercise for the reader.

Update: The reason (amongst others) why your regex did not work is because the web-page has a lot of spurious linefeeds and other strange white-space embedded.