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

use IO::All;

my @data;
while (<>) {
    chomp;
    if (/(.*)0[2-5]\/02\/2018/s) {
	io('out.txt')->appendln($_);
    }
} continue {
    close ARGV if eof;  # Not eof()!
}

__END__

$ perl test.pl in.txt && cat out.txt 
XA29EN35   M4C6M       D7F577Q  111.222.333.123 AWAY - [02/Feb/2018:01:08:39 -0800]        02/02/2018
JK20TQ67   K1L0V       T6Z148X  111.222.333.123 HOME - [03/Feb/2018:01:08:39 -0800]              03/02/2018
SO78NZ28   B5S8J       W9F920Z  111.222.333.123 HOME - [04/Feb/2018:01:08:39 -0800]          04/02/2018
BI55SY64   R6P5H       A9U757R  111.222.333.123 HOME - [05/Feb/2018:01:08:39 -0800]              05/02/2018