I may have a solution but I don't know if it will have any other side effects, it appears to work.    In the login.ascx.vb in desktopmodules\admin\authentication  I modifed the following code, I added  this to the if statement.  complete Modified code is below.

               ElseIf PortalSettings.UserRegistration = PortalRegistrationType.PrivateRegistration Then
                    'Pass return url to register as original url  and return to this control to login after regsitration
                    Response.Redirect(RegisterURL(ReturnUrl, Null.NullString), True)
  

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

        Private Sub cmdRegister_Click(ByVal sender As Object, ByVal e As EventArgs) Handles cmdRegister.Click
            If PortalSettings.UserRegistration <> PortalRegistrationType.NoRegistration Then
                Dim ReturnUrl As String = NavigateURL()
                If Not String.IsNullOrEmpty(Request.QueryString("returnurl")) Then
                    ReturnUrl = Request.QueryString("returnurl")
                End If
                ReturnUrl = HttpUtility.UrlEncode(ReturnUrl)

                If PortalSettings.UserRegistration = PortalRegistrationType.PublicRegistration Then
                    'Pass return url to register
                    Response.Redirect(RegisterURL(ReturnUrl, Null.NullString), True)
                ElseIf PortalSettings.UserRegistration = PortalRegistrationType.VerifiedRegistration Then
                    'Pass return url to register as original url  and return to this control to login after regsitration
                    Response.Redirect(RegisterURL(ReturnUrl, Null.NullString), True)
                ElseIf PortalSettings.UserRegistration = PortalRegistrationType.PrivateRegistration Then
                    'Pass return url to register as original url  and return to this control to login after regsitration
                    Response.Redirect(RegisterURL(ReturnUrl, Null.NullString), True)
                End If
            End If
        End Sub

Hi!
I'm facing the same issue in a DNN 05.01.01. When I use a public registration the module works. But if I turn it to be private, the register link just refresh the page.
Do you know if this was fixed in newer versions of DNN? 

Thanks,

Janise Piombo