Try catching those sequences which can't be downloaded. You can catch the BioPerl $obj->throw(); method from Bio::Root::root with a simple eval block.
Try something like this: (Not tested)

#!usr/bin/perl


use English '-no_match_vars';
use strict;
use warnings;

use Bio::Perl;

my $database   = 'genbank';
my $format     = 'fasta';
my @accessions = ( "bunch", "of", "accession", "numbers");

for my $i ( 0 ... 2000 ) {

   my $entry_id = $accessions[$i];

   eval {
        my $sequence = get_sequence($database, $entry_id);
        write_sequence( '>-', $format, $sequence );
   };
 
   if ( $EVAL_ERROR ) {
      # Log Error here if an error occured
      print {*STDERR} "Could not download sequence: [$entry_id]\n";
   }


   # If you need to keep track of count
   my $count = $i + 1;

}
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J,