Well, I can get it to work by bringing the lexical scope outside the loop:

use strict;
use warnings;

use Data::Dumper;

my @file_names = qw(
   /a/990101ag/toc.html
   /a/20000115/toc.html
   /a/990115ag/toc.html
);

my %date;
for my $file_name ( @file_names ) {
   print "Now working on $file_name\n";

   %date = ( YEAR => '', MONTH => '', DAY => '' );
   $file_name =~ m#
      (?<=/a/)
      (\d{2,4})(\d{2})(\d{2})(?:ag)?
      (?=/)
      (?{ @date{'YEAR', 'MONTH', 'DAY'} = ( (
         length($1) == 2
         ? '19' . $1
         : $1), $2, $3
       ) })
      (?{ print "Here, \%date is populated (joined): ", 
                join('-', @date{'YEAR', 'MONTH', 'DAY'}),
                "\n"
       })
   #x;

   print "But after the first iteration, ",
         "it isn't populated here (joined): ",
         join('-', @date{'YEAR', 'MONTH', 'DAY'}),
         "\n";
   print Dumper(\%date);

   print "\n\n";
}
[download]

This looks like some unusual interaction between lexicals and the regex engine.

Update: cleaned up an initialization.