Pretty sure what you have is botrytis blight, aka grey mold.
http://www.gardeningknowhow.com/plant-p ... blight.htm
Botrytis blight on plants is caused by Botrytis cinerea, a fungus that attacks tender parts of the plant in the presence of high humidity. Botrytis blight symptoms on flowers include spotting, discoloration and wilting. Buds often fail to open. It may look as though the flowers are old and fading.
You can tell the difference between an old flower and one affected by botrytis blight by the pattern of discoloration and wilting. Browning from normal aging begins with the petals on the outer edge of the flower. If browning occurs on inner petals first, the cause is probably botrytis blight. Leaves and shoots with botrytis blight have brown lesions and masses of gray spores. Severely affected leaves and shoots die back, and the leaves drop from the plant. Fruit also rots and drops off.
The "webbing" kind of stuff is the grey spores and spore forming bodies.
The article linked talks about prevention and a little about treatment. But unfortunately, especially when the disease is this advanced, no treatment is likely to be very effective. It's just an annual. I would destroy the infected one and then treat the other one with some kind of anti-fungal (baking soda solution or hydrogen peroxide are organic choices) to try to prevent it from getting infected. Your sick one has been sending out spores for awhile now, so the other one is definitely at risk.