what would it take for Avogadro's theory to be discarded?

Question

and what would happen if it did become discarded?

Answer 1

It would take a better theory. Avagadro's number (which was not "discovered" by Avagadro but named after him by the guy who came up with it) has proven itself a useful predictive thing for many many years in many many many different chemical reactions. The concept for the number was very important in humankind's evolving understanding of the world of atoms, elements, molecules, chemical reactions, etc.

If you could come up with a significant improvement, you would probably win a Nobel prize. Given the complexity of quantum mechanics and the gory details of how subatomic particle behave, there may very well be room for a dramatically new theory.

I hope this helps.