Have you tried creating a new Net::POP3 object for each user?

i.e.

use strict;
use Net::POP3;

$|++;

my %user = ( a => 1 , b => 2, c => 3);

my $host  = "host.net";
for my $key ( keys %user){
  my $pop   = Net::POP3->new($host);
  print "Working on $key...\n";
  my $msg = $pop->login( $key, $user{$key} );
  print "$key: $msg\n";
  $pop->quit;
}
[download]

I haven't used Net::POP3 at all but it might be worth a try.