How long does athlete's foot fungus survive on objects like shoes and floors?

Depends: It depends if the floors/shoes are wet/moist or dry. Fungus doesn't like dry climates but absolutely loves warm, moist areas like a locker room floor or a shoe.

Keratin: Fungus lives on keratin, which is in the epithelial lining of the skin. Skin cells are also shed and keratin is present in the environment. Fungi can go into dormant state and live for years.