Having added more error checking to see what's going on with the line it's having trouble with:

        if(!$rss) {
            print " -- Feed is broken -- \n";
            my $error = $parser->errstr;
            print $error . "\n";
            $error =~ /Ln: (\d+),/;
            my $line = $1 - 1;
            print "Line $line\n";
            my @file_array = split("\n", $feed);
            print length($file_array[$line]);
            print $file_array[$line] . "\n";
            next FEED;
        }
[download]

I see:

 -- Feed is broken -- 
End tag mismatch (ttl != ) [Ln: 5, Col: 642255168120818]

Line 4
15              <ttl>60</ttl>
[download]

So what it appears to be seeing in that line matches what I'm seeing in the archived version, which makes sense. It's 15 characters long and not 642255168120818, and definitely has the closing tag. So what's going wrong?