You're looping on input from your log file. I expect that you meant to loop on input from STDIN. Also, you need to update your timestamp variables inside the loop. Try this:

use strict;
use warnings;
use Data::Dumper;

my $table;

my $log = 'log_file.txt';


open my $fh, '>>', $log or die "Can't open $log : $!";

while (<STDIN>) {

    my $comment = $_;
    chomp $comment;
    my ($sec,$min,$hour,$mday,$mon,$year,$wday,
        $yday,$isdst)=localtime(time);

    printf "%4d-%02d-%02d %02d:%02d:%02d\t",
    $year+1900,$mon+1,$mday,$hour,$min,$sec;

    print $comment . "\n";

    printf $fh "%4d-%02d-%02d %02d:%02d:%02d\t",
    $year+1900,$mon+1,$mday,$hour,$min,$sec;

    print $fh $comment . "\n";

}

close $fh;
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