Well it works for me. When I run:

#!/usr/bin/perl -w

use strict;
use CGI qw(:standard);

print STDERR "TEST";

print header(),start_html(),"foo";
[download]

I get 'TEST' in my error log as I expect. It is difficult to know what is going on for you without more information but I would suspect that you are running the program under mod_perl although I am not sure how the die() would work under that circumstance.

/J\