I would use NCBI's efetch service for this. To access this service you can write your own script to perform the request or use BioPerl. Since you are using BioPerl I would recommend Bio::DB::EUtilities. Here is an example:

use strict;
use warnings;
use Bio::DB::EUtilities;

my @ids = qw(ADE06225 KJU84168 CEJ19818 AEG68532);

my $factory = Bio::DB::EUtilities->new(-eutil   => 'efetch',
                                       -db      => 'protein',
                                       -rettype => 'fasta',
                                       -email   => 'mymail@foo.bar',
                                       -id      => \@ids);

my $file = 'myseqs.fasta';

# dump HTTP::Response content to a file (not retained in memory)
$factory->get_Response(-file => $file);

If you want genbank, just change the return type to gb or whatever format you want. If you want to split the individual records returned instead of having them all in one file, this can easily be done with Bio::SeqIO. Check out the EUtilities HOWTO and the EUtilities Cookbook for more examples and explanation.

Also, please avoid cross-posting (I noticed you posted on PerlMonks also). This is fine if there are no responses but it is generally discouraged and seen as a misuse of people's time.

I wouldn't be surprised if there is a batching method in place in bioperl already, but using just basic perl you can loop very easily with something like this:

use Bio::DB::GenBank;
my $gb=new Bio::DB::GenBank;

my $infile = $ARGV[0];    # first argument after the script is a text file of IDs, one per line
open(IN, "$infile") or die "Unable to open $infile: $!";  

while (<IN>){
    my $id = chomp($_); 
    my $seq= $gb->get_Seq_by_id ('$id');
    write_sequence (">roar.fa", 'fasta',$seq );
}

I haven't tested this but it should get you close. I recommend reading up on loops in perl to see how to do this properly.

1. This is a programming question
2. Look up file reading and loops in Perl