"but this doesn't..."

use LWP::UserAgent ();
use DBI;
use parent 'HTTP::Message';
$mess = HTTP::Message->new();
$mess->encode(gzip,deflate);
my $ua = LWP::UserAgent->new(timeout=>10);
$mess = HTTP::Message->new();
$mess->encode(gzip,deflate);
$ua->default_header('Accept Encoding'=>$mess=HTTP::Message->new());
$ua->default_header( USER_AGENT =>'COMPANY admin@example.com' );
my $SQL = "select url,filename from linktable";
my $sth = $dbh->prepare($SQL) or die "Prepare".$dbh->errstr;
$sth-> execute() or die "".$dbh->errstr;
while (my $row = $sth->fetchrow_arrayref) {
my ($url,$filename)= ($row->[0],$row->[1]);
print "\n$row[0] $row[1]\n";
my $resp = $ua->mirror( $url,$filename);
 if ( $resp->{success} ) {
        print "OK\n";
    }
    else {
        print "Failure: $resp->{status}, $resp->{reason}\n";
    }
}
[download]

no strict, no warnings, no creation of a database handle object, it's almost as though you've ignored everything 1nickt has provided in this thread...

The error I am getting is 403 forbidden.

so the issue is not with the database related code. it is with the HTML::Tiny or LWP settings.

here is the output with use warnings on

Unquoted string "gzip" may clash with future reserved word at testdown
+.pl line 9.
Unquoted string "deflate" may clash with future reserved word at testd
+own.pl line 9.
Unquoted string "gzip" may clash with future reserved word at testdown
+.pl line 30.
Unquoted string "deflate" may clash with future reserved word at testd
+own.pl line 30.
Unquoted string "gzip" may clash with future reserved word at testdown
+.pl line 33.
Unquoted string "deflate" may clash with future reserved word at testd
+own.pl line 33.
Failure: 403, Forbidden
Failure: 403, Forbidden
Failure: 403, Forbidden
Failure: 403, Forbidden
Failure: 403, Forbidden
[download]

These is what Securities and Exchange Commission says about downloading from them

Fair access
Current max request rate: 10 requests/second.
To ensure everyone has equitable access to SEC EDGAR content, please u
+se efficient scripting. Download only what you need and please modera
+te requests to minimize server load.

SEC reserves the right to limit request rates to preserve fair access 
+for all users. See our Internet Security Policy for our current rate 
+request limit.

The SEC does not allow botnets or automated tools to crawl the site. A
+ny request that has been identified as part of a botnet or an automat
+ed tool outside of the acceptable policy will be managed to ensure fa
+ir access for all users.

Please declare your user agent in request headers:

Sample Declared Bot Request Headers:

User-Agent:

Sample Company Name AdminContact@<sample company domain>.com

Accept-Encoding:

gzip, deflate

Host:

www.sec.gov
[download]

The line numbers you've posted errors at don't exist in the code you've posted. The sensible approach is to post a SSCCE when asking for help.

$mess = HTTP::Message->new();
$mess->encode(gzip,deflate);
my $ua = LWP::UserAgent->new(timeout=>10);
$mess = HTTP::Message->new();# Again
$mess->encode(gzip,deflate); #   ?
[download]

Why are you doing this twice? Why not take steps to fix problems before posting code here? With strict/warnings:

marto@Marto-Desktop:~/code/perlmonks$ perl -c junk.pl 
Global symbol "$mess" requires explicit package name (did you forget t
+o declare "my $mess"?) at junk.pl line 6.
Global symbol "$mess" requires explicit package name (did you forget t
+o declare "my $mess"?) at junk.pl line 7.
Global symbol "$mess" requires explicit package name (did you forget t
+o declare "my $mess"?) at junk.pl line 9.
Global symbol "$mess" requires explicit package name (did you forget t
+o declare "my $mess"?) at junk.pl line 10.
Global symbol "$mess" requires explicit package name (did you forget t
+o declare "my $mess"?) at junk.pl line 11.
Global symbol "$dbh" requires explicit package name (did you forget to
+ declare "my $dbh"?) at junk.pl line 14.
Global symbol "$dbh" requires explicit package name (did you forget to
+ declare "my $dbh"?) at junk.pl line 14.
Global symbol "$dbh" requires explicit package name (did you forget to
+ declare "my $dbh"?) at junk.pl line 15.
Global symbol "@row" requires explicit package name (did you forget to
+ declare "my @row"?) at junk.pl line 18.
Global symbol "@row" requires explicit package name (did you forget to
+ declare "my @row"?) at junk.pl line 18.
junk.pl had compilation errors.
[download]

Update: also it's good form to mark significant updates to a post.

"These is what Securities and Exchange Commission says about downloading from them"

I know.