Friend declaration grants access only to some members

In the following code, all specializations of the Derived class should be friends of each other. It works to some extent; however, the friend declaration seems to grant access only to some members.

class Base { protected: int i; };
template <typename T> class Derived;
template <typename T> class Derived<Derived<T>> : public Base {
  template <typename U> friend class Derived;
  int i;
 public:
  void f() {
    Derived<Derived<float>> d;
    (void)d.i;       // works fine, although i is private
    (void)d.Base::i; // error: 'int Base::i' is protected
  }
};
int main() { Derived<Derived<int>>().f(); }

Why can Derived<Derived<int>> access Derived<Derived<float>>::i (which is private member) but not Derived<Derived<float>>::Base::i (which is a protected member)?

I suspect the problem may have to do with the fact that a partial specialization is involved. However, strictly speaking, the friend declaration does not declare a partial specialization. Moreover, if the partial specialization was the reason, why does d.i still work?

In short, why does d.i work but not d.Base::i and how to fix it?