I tried this myself with Archive::Tar 1.44 on an ubuntu box and got out of memory almost straight away:

use strict;
use warnings;
use Archive::Tar;
use Devel::Leak;


my $handle;

my @results = qw ( u1.tar.gz u2.tar.gz u3.tar.gz u4.tar.gz u5.tar.gz u
+6.tar.gz u7.tar.gz u8.tar.gz u9.tar.gz u10.tar.gz );
foreach my $tar_file ( @results ) {
  my $count = Devel::Leak::NoteSV($handle);
  print $count,"\n";
  my $x = Archive::Tar->new or die "Failed to get tar object";
  my $extracts = $x->read($tar_file);
  print "extracts $extracts\n";
  $x->clear;
  undef $extracts;
  print Devel::Leak::CheckSV($handle), "\n";
}
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with 10 tar.gz files in the current directly all the same and of size 6.2Mb it fails with out of memory after only one:

~/tmp$ perl t.pl
28447
extracts 1
new 0x85fdce0 : 
new 0x85fdcec : 
loads and loads of these
old (1):
 0 
old (1):
 0 
quite a lot of those
28647
28649
Out of memory!
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Tracking it through it failed in

Archive::Tar::_read_tar(/usr/local/share/perl/5.8.8/Archive/Tar.pm:318
+):
318: my $offset = eval { tell $handle } || 'unknown';
  DB<1> 
Out of memory!
[download]

So does that imply it is a problem with Archive::Tar module?