No, you don't need two statement or database handles. Do you know what the $ID is when the statement fails? You're iterating over @$clusters but grabbing $ID's from @units. Maybe $ID is undef? I'd use placeholders something like this (with maybe some extra error handling in case nothing is selected into @row...which would be easy, just remove the "1" from the code below):

my $sth = $dbh->prepare("select * from finalLevel3 where id=?");
foreach $item (@{$clusters}) {
    $ID = $units[$i][0];
    unless (eval {
      @row = $dbh->selectrow_array($sth, undef, $ID);
      1
    }) {
      die "Error on ID [$ID]: $@";
    }

    # convert the mysql result back to a string again
    $promoter_line = join "\t", @row;
    $promoter_line .= "\n";
   
    $parser_hash{$item} .= $promoter_line;
    $i++;
}
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