Doesn't work in Portuguese (pt-br): "Sorry, you've reached the maximum number of invitations."

Indeed, same message for fr-FR either.
I'm going to investigate, to see if I can suggest a quick fix.

Ok, I fixed it by creating a new Role, and by adding this role to the users.
The code seems buggy for the built-in roles.

Hi,
To fix the bug,

I create a new user role (you can name it as you want, let's call it "Members" for this case)
(To do it, I go to Administer -> Users settings -> Roles and create the role)
Then you have to add proper permissions for the role, in order to send invitations.

Then you have to go to the user list, select the users you want to grant the power to send invites, and chose the option to add the Members role to the users.

Is it what you've done ?

Excellent question :)
Looks like we have to do it manually until a new version is released.

Besides, I've found some code in the module that checks the number of invites a user can send. (This code is bugged and prevents an authenticated user to invite)
I can only remove the invites limit, but I can't control the number of invites allowed per user.
Maybe you'll want to see how it can be done ?

Also, you can use the Auto Assign Role module.

This error still exist (using the latest dev (6.x-2.x-dev)).

This caused by invite_get_role_limit() which check $account->roles that are not translated against user_roles!!!

  foreach (user_roles(0, 'send invitations') as $role) {
    $role_no_space = str_replace(' ', '_', $role);
    if (in_array($role, $account->roles)) {
      $role_max = variable_get('invite_maxnum_'. $role_no_space, INVITE_UNLIMITED);
      if ($role_max == INVITE_UNLIMITED) {
        return INVITE_UNLIMITED;
      }
      $role_limit = max($role_max, $role_limit);
    }
  }

Suppose better to convert this to role_id to remove confusion with translatable role names in multilingual sites

Here is a first quickfix but I still wants to make patch to change role name to RID

Patch with upgrade path from old settings. Needs review mostly with modules that can use old settings style.

Current variable names does not working with multilingual sites bacause user_roles() always translate authenticated rolename

      case DRUPAL_AUTHENTICATED_RID:
        $roles[$role->rid] = t($role->name);
        break;

Duplicate of #322748: Only administrator can send invitations on multilingual installation.