I don't understand why we still need to move the initialization of the seqIO outside the loop?

Well did you try it.... You can write it this way since there is no need to initialize the SeqIO object each time since you are resetting the filehandle. I expect it is a miniscule performance different.

#!/usr/bin/perl -w
use strict;
use Bio::SeqIO;

my $file = $ARGV[0];
open INFILE, "<$file" or die "$0:  Can't open file $file: $!";
my $in = Bio::SeqIO->new(-format => 'fasta', 
                         -noclose => 1, 
                         -fh => \*INFILE);

for (my $trial = 1; $trial <=2; $trial++)
{
   seek(INFILE,0,0);
   print "Trial $trial\n";

   my $i =1;
   while( my $seq = $in->next_seq()  ) {
      print $i++, " : ", $seq->seq(), "\n";
   }

}
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As for the -noclose option, Bio::SeqIO ISA Bio::Root::IO so see the documenation for that module. Unfortunately perldoc does not allow one to pull in documentation from inherited modules so you have to read around to get the full list. The Pdoc generated documentation at our site doc.bioperl.org does have links up the inheritance hierarchy so you read the docs for the superclasses. So anything you can do with a Bio::Root::IO you can do with a Bio::SeqIO object. All the other Bio::XXIO modules also inherit from Bio::Root::IO.