It's hard to answer as I can't reproduce (ok, ok it's also beccause I'm just an initiate... ;-)
It just works fine for me: I got the content-length
Does it always fail ? or just on one file ? or (apparently) randomly ?
Is there a possibility that you mis-type the filename or something like that ?
(Don't feel offended!)

Anyway I've slightly modified your code (to check other things (LWP debug code+ the full header to see what was returned...) What's the result when you execute this:
(replace the filename)

require LWP::UserAgent;
use LWP::Debug('+');

$ua = new LWP::UserAgent;

$request = new HTTP::Request('HEAD',
'http://content.emusic.com/demo/542259/Guitar_Slim-Sufferin_Mind-01-Th
+e_Things_That_I_Used_To_Do-demo.mp3');

$response = $ua->request($request);

my %headers=%{$response->headers};


print "dooh" if !defined($response->headers->content_length);

for my $value (keys %headers) { print "($value)=($headers{$value})\n";
+ }
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