'code' should only be used once. Once the 'code' is used to obtain the 'access_token', store the 'access_token' to the session. Use 'access_token' if available in the session.

backends.py

from django.contrib.auth.models import User
from facebookconnect.models import FacebookProfile
from django.conf import settings
from django.core.urlresolvers import reverse
import facebook
from facebookconnect.utils import facebook_login_check, get_access_token


class FacebookConnectBackend:
    """
    Authenticates against django.contrib.auth.models.User.
    """
    @ staticmethod
    def authenticate(request):

        cookie = facebook_login_check(request.COOKIES)
        if cookie:
            facebook_user_id = cookie["uid"]
            access_token = cookie["access_token"]

        elif 'access_token' in request.session:
            access_token = request.session['access_token']
            graph = facebook.GraphAPI(access_token)
            profile = graph.get_object("me")
            facebook_user_id = str(profile["id"])

        elif request.GET.has_key('code'):
            url = reverse('facebookconnect_authenticate')
            next_url = request.GET.get('next', None)
            if next_url:
                url = '%s?next=%s' % (url, next_url)
            access_token = get_access_token(request.GET['code'], url)
            request.session['access_token'] = access_token
            graph = facebook.GraphAPI(access_token)
            profile = graph.get_object("me")
            facebook_user_id = str(profile["id"])

        else:
            return None
        
        try:
            fb_profile = FacebookProfile.objects.get(facebook_id=facebook_user_id)
            fb_profile.user.backend='facebookconnect.backends.FacebookConnectBackend' 
            fb_profile.access_token = access_token
            fb_profile.save()
            return fb_profile.user
        except FacebookProfile.DoesNotExist:
            return None       

    def get_user(self, user_id):
        try:
            return User.objects.get(pk=user_id)
        except User.DoesNotExist:
            return None

views.py

def fbc_authenticate_backend(request, next_url=None):

    #import ipdb; ipdb.set_trace()
    user = FacebookConnectBackend.authenticate(request)
    message = ''
    created = False

    authenticated = False
    created = False
    
    if user is None:

        cookie = facebook_login_check(request.COOKIES)
        if not cookie and not request.GET.has_key('code'):
            return False, user, created
        
        
        if not cookie:
            #code = request.GET['code']
            #redirect_uri = '%s%s' % (settings.DOMAIN, reverse('facebookconnect_authenticate'))
            #access_token = get_access_token(code, redirect_uri)
            access_token = request.session['access_token']
        else:
            access_token = cookie["access_token"]