Are you using BASIC or FORM authenticator? If you share your code, it may be easier for other to see what might go wrong.
Also, LWP is not a browser so it can behave differently to a browser.
Purely based on your code shown above and the returned HTTP code, I would suggest you replace "workitems.json" with "workitems" and add an HTTP header "Accept: application/json" to request a JSON response.

I did investigate more and it get weirder. Let's start with the code:

! /usr/bin/perl

use strict;
use DBI;

use lib ("/home/matteau/JSON-2.53/lib"); # So we can find json
use JSON; # imports encode_json, decode_json, to_json and from_json.

For LWP (https requests to RTC)

use LWP::UserAgent;
use HTTP::Request::Common;
use HTTP::Cookies;
use HTTP::Headers;

Usefull for printing structures for debugging

use Data::Dumper;

my $pw = "asdaa"; # not the real one :-)

my $RTC_USERID = "matteau";



my ($response, $response_string);
my $HOST_PROD = "https://PROD.com:9443/jazz";
my $HOST_TEST = "https://TEST.com:9443/jazz";

my $HOST = $HOST_TEST;

Need cookies for HTTPS

my $userAgent = LWP::UserAgent->new(agent => 'perl get');
$userAgent->cookie_jar({});

Authenticate

$response = $userAgent->request(POST "$HOST/authenticated/j_security_check?j_username=$RTC_USERID&j_password=$pw");

Looks like we need a code of 302 followed by checking the location

field for the https negotiation

if($response->code == 302) {
  if($response->header('location') =~ m,/authfailed$,) {
    print "Login failed\n";
    #      print Dumper($response);
    die "ERROR: RTC authentication failed ";
  } else {
    print "Login sucessful\n";
  }
} else {
  print "j_security_check failure response : $response->as_string\n";
  die "ERROR: RTC: j_security_check failure ";
}

Get WIs in a range

FAIL

$response = $userAgent->request(GET "$HOST/oslc/contexts/_NmIe8D8qEd6jzOcwVhPAgw/workitems.json?oslc_cm.pagesize=1000&oslc_cm.properties=dc:identifier&oslc_cm.query=dc:modified>=\"2013-11-30T00:01:59.000000Z\" and dc:modified<=\"2013-12-02T15:33:29.873500Z\"");

PASS

$response = $userAgent->request(GET "$HOST/oslc/contexts/_NmIe8D8qEd6jzOcwVhPAgw/workitems.json?oslc_cm.pagesize=1000&oslc_cm.properties=dc:identifier&oslc_cm.query=dc:modified>=\"2013-11-30T00:01:59.000000Z\" and dc:modified<=\"2013-12-02T15:33:29.873499Z\"");

if($response->is_success) {
  print "success\n";
  $response_string = $response->content;
} else {

  my $junk = $response->code;
  print "code\t\t=>$junk<=\n";
  print "\n\n\n";
 
  die "TEST FATAL ERROR in response from RTC";
}

my $base = decode_json $response_string;

my $ret = $base->{"oslc_cm:totalCount"};

RTC only return 1000 results, need shorter date range if it is exceeded

if ($ret > 1000) {
  print "INFORMATION: $ret items available but only 1000 returned\n";
} else {
  print "$ret items returned\n";
}

exit;

Look at the pass and fail example. The pass one returns 100 WI. The fail one return a code of 406. The only difference between the queries is the end time; it pass at .873499Z and fails at .873500 (the smallest increment possible to the end time). I doubt that 1000 work items got modified in the mean time...

Any idea?

Thanks...