looks to me like the varnish has failed and water has got in. Varnish is quite brittle and IMO not suitable for outside work. It can even crack from normal weather-caused expansion and contraction, especially if it faces the sun. Wooden boats have to be rubbed down and redone every year or two, and are prone to this black fungal staining.
A better method:
sand off the varnish and damaged wood
use bleach to remove the staining if necessary.
dry it thoroughly
Treat it with several coats of Cuprinol Clear wood preserver (to combat future fungal or insect attack)
Dye it with Colron if you want to change the colour or hide the staining
Treat it with several coats of boiled linseed oil. Thin the first few with white spirit to help it soak in. After each coat, wipe off any excess that has not soaked in after half an hour or so. Wet the rags with water and tie up in a plastic bag or they may self ignite (this is not a joke). This gives a water-repellent treatment that does not go hard enough to crack, and as it has soaked into the wood, will not let water in if the surface is chipped or scuffed e.g. by people clumping through it in heavy boots. Some people prefer Tung oil, which I have not tried.
You might also consider protecting a wooden doorstep with a brass or copper threshold which can be bent to fit. This was common on Victorian and Edwardian houses of good quality to get over this very problem.
p.s. as Joes says, the edges of doors, especially the bottom, are most in need of good protection, and most often don't get it. You might consider lift-off hinges to make the job easier.
