The problem is that e() always returns a different hash reference, for which each always returns the "first" pair.

You can work around that by memoizing e(), but I don't know if that's applicable for what you want to do:

use warnings;
use strict;
use Memoize;
memoize('e');
sub e() {
  my %result=(A=>1,B=>2);
  wantarray ? %result : \%result;
}
my %env=e;
$|=1;
while (my ($var,$val) = each %env) {
      print "(hash) $var=$val\n";
}
while (my ($var,$val) = each %{ e() }) {
      print "(ref)  $var=$val\n";
}
[download]

P.S. Please don't use &e to call a sub, use e() instead - you might get surprising results otherwise.

Update: or simply assign the ref to a temporary variable: my $e = e(); while (my ($k, $v) = each %$e){...}