Cinematographic film has a layer of gelatin on its surface. This emulsion layer is where the image is formed but also provides ideal food for fungi like Aspergillus and Penicillium. If the fungus forms a layer of mould on a film it produces enzymes which allow it to use the film as food and to grow. So the damage it can cause is irreversible as the mould "eats" the image stored on the film's surface.
You can read more at http://www.bbc.co.uk/news/science-environment-11202019
I am curious if the same problem affects microfilms. The article by Pamela Rutherford does not mention microfilm, but does say the fungus "can affect any type of film. It comes down to how it's been stored..."
The article recommends storing "master film at sub zero temperatures and at around 35% relative humidity." That's not the temperature typically used to store most microfilm masters.