Why does storing references (not pointers) in containers in C++ not work?

Not directly relevant to the "why", but to give an answer to the implied desire to do this, I would mention that the c++11 standard library has std::reference_wrapper to enable this. It is implicitly convertible to a reference and it is storable in standard containers.

As Containers store objects and references are not objects. In case you are at c++ 11, you can use std::reference_wrapper to wrap things to assignable objects.

http://en.cppreference.com/w/cpp/utility/functional/reference_wrapper

std::reference_wrapper is a class template that wraps a reference in a copyable, assignable object. It is frequently used as a mechanism to store references inside standard containers (like std::vector) which cannot normally hold references.

Containers store objects. References are not objects.

The C++11 specification clearly states (§23.2.1[container.requirements.general]/1):

Containers are objects that store other objects.