As others have noted, you need to modify $month to reflect that timelocal expects it to be 0 based (0 = january, 11 = december). Also, your older_than_MAX_AGE is overkill. Here is how I would implement it:

#!/usr/bin/perl -w 
 
use strict; 
use Time::Local; 
use constant MAX_AGE => 20; 
 
 
sub _convert_date { 
    # This takes a date in YYMMDD format and converts it to epoch  
    # seconds (assumes 12:00:00 midnight) 
    my $date = shift; 
    my ( $year, $month, $day ) = ( $date =~ /(\d\d)(\d\d)(\d\d)/ ); 
    $year += 2000; 
    $month--; 
    timelocal( 0,0,0,$day,$month,$year ); 
} 
 
sub older_than_MAX_AGE { 
  my $date=shift; 
 
  time-(MAX_AGE*86400) > $date; 
} 
 
print older_than_MAX_AGE(_convert_date("010401")),"\n"; 
print older_than_MAX_AGE(_convert_date("010411")),"\n";
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Note that this doesn't require any additional modules other than Time::Local which you apparently already have installed and are using.