Most likely, you have lost (or bent) a very tiny spring that is used to complete the circuit.
The piezo plate is bonded to the rear case; a part of the arm that retains the battery reaches up and contacts the rear case when the rear case is attached. The other half of the circuit, from the center-portion of the piezo crystal to the circuit board, is made via a tiny tiny tiny spring. (See a picture of a Casio contact spring doing the same job
here.) In the Rado Multis that I have looked at, that spring rests loosely on a "pin" (and is therefore very easy to lose after the back is no longer holding it in place.)
Look for a cutout in the backplate of the watch mechanism, inside which is a gold pin or post that doesn't quite reach past the backplate. There's supposed to be a spring, resting loosely on this post, which (when the back is attached) reaches past the backplate to make contact with the center terminal area of the piezo.
If you're lucky, it's still in there, and bent or something. If it's missing entirely, you'll have to search out a replacement, or a watch repair that has them.