The following works for me:

#!/usr/local/bin/perl
use warnings;
use strict;

sub do_program {
    print "Please wait for a timeout....\n";
    <STDIN>
}

my $timeout = 5;
eval {        
    local $SIG{ALRM} = sub { die "alarm\n" }; 
    alarm $timeout;        
    &do_program(1, 100);        
    alarm 0;    
}; 

if($@) {        
    print "$@<BR>\n";
}
[download]

Also on Linux 2.6.18.
You don't give details of what do_program is actually doing. If, as the name implies, it is running another process, then you should be aware that pending alarms are cleared in a child process. This is a UNIX feature, not anything to do with Perl. It then depends on how you are actually running the external process, and how you are waiting for it.

Proc::Background might help, it has a timeout feature.

Update: it occurs to me that, because of your use of <BR> in the print statement, you might be running under mod_perl. There are some notes concerning alarm here: http://perl.apache.org/docs/2.0/user/coding/coding.html.