Update: You do realize you are never incrementing $i in the while loop, making it an infinite while loop? And maybe the writes to the file are being buffered so you do not see anything right away. How long have you left it running?

Here is a short subroutine I like to use that is based on what Stein (CGI.pm) recommends in "Network Programming with Perl". As you can see, there are several additional things you should be doing for your script to be a proper daemon. I have seen forking multiple times before, but I do not think that is actually necessary. It's probably a more expensive, less elegant way to e.g. help disassociate from the shell. Though if you want to you could also call daemonize() more than once.

use IO::Socket;
use POSIX qw(WNOHANG setsid);

sub daemonize {
        $SIG{CHLD} = 'IGNORE';        # Configure to autoreap zombies
        die "Can't fork" unless defined ( my $child = fork );  # FORK 
+<<<<<<<<<<<<
        CORE::exit(0) if $child;      # Parent exits
        setsid();                     # Become session leader
        open( STDIN,  "</dev/null" ); # Detach STDIN from shell
        open( STDOUT, ">/dev/null" ); # Detach STDOUT from shell
        open( STDERR, ">&STDOUT"   ); # Detach STDERR from shell
        chdir '/tmp';                 # Change working directory
        umask(0);                     # Reset umask
        $ENV{PATH} = '/bin:/sbin:/usr/sbin';  # Reset PATH
        }
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See also Re: Persistent perl.