According to WebMD, an infection called mange, which is caused by an infestation of mites, causes a dog to lose hair around its eyes. Ringworm, allergies and Cushing's disease can also create bald spots.
The ASPCA points out that mange is a skin disease caused by mites that results in hair loss. There are many ways that dogs contract this disease though the most common cause is transmission from mothers to pups during the first few days following their birth. One type of mange, called localized demodicosis, occurs commonly in puppies and affects the faces, resulting in hair loss around the eyes. This type of mange usually clears up on its own. The second type of mange, generalized demodicosis, affects the dog's entire body. Besides causing hair loss, it also causes itchiness and bacterial infections. The third type of mange, demodectic pododermatitis, occurs only on the feet. While most dogs have mites, they do not all develop mange because they are healthy.
WebMD states that allergies also cause hair loss because the dog rubs at the irritated area. Ringworm is a fungal infection, which is characterized by the red, crusty circular rings in the dog's skin in addition to hair loss. Cushing's disease occurs when a certain hormone is overproduced, causing hair loss.