My anonymous brother is quite right. You can avoid this sort of problem (where by you test one thing but actually report another) by using a variable name for both. eg.

      my $file = "/strek/$race/logs/rlog$i.sr.html";
      if ( -s $file ) {
         next;
      } else {
         print "$file either does not exist or is 0 bytes!\n";
      }
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Other things you could do include making more use of the $ldir variable and rolling the second loop into the first.

#!/usr/bin/perl

use strict;
use warnings;

my $ldir = '/strek';
my @races = undef;

opendir my $dh, $ldir
   or die "$0: opendir: $!";

while (defined(my $name = readdir $dh)) {
   next unless -d "$ldir/$name";
   push (@races, $name);
   for my $i (0..4) {
      my $file = "$ldir/$name/logs/rlog$i.sr.html";
      if ( -s $file ) {
         next;
      } else {
         print "$file either does not exist or is 0 bytes!\n";
      }
   }
}

# Now do something useful with @races here
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