"when no evident cause for sleeplessness can be found in an infant, the possibility of milk allergy should be given serious consideration."
Cow's milk is a convenient way to get all the protein and fat you need for development, but it is a convenience not a necessity. And if you are intolerant to cow's milk, you might be drinking it, but you might not be absorbing the nutrients.
I would advise ANY non sleeper after 12 months old to give up wheat/dairy and soy for a few days to see if they have a part in the terrible sleeping situation. Especially if crying it out doesn't work. Rice milk with a little coconut milk in it is a great dairy free, creamy treat to try. And coconut milk is full of lauric acid which is only found in coconut and breastmilk. With enough protein at meals*** your child will thrive. One year olds don't need cow's milk, they need lauric acid, healthy saturated fats for brain development and some protein, vitamin D and calcium for growth which you can get in rice milk or fortified orange juice.
Also, Dr. Morton Teich, New York Environmental Allergist from Mt. Sinai hospital in NYC told me, you often crave the things you are most allergic to. So a child who is a picky eater who will only eat wheat (pasta, bread and goldfish) might have a wheat or gluten intolerance. Or a child who guzzles lots of milk might be intolerant of dairy.
The industrialization of our food supply has made milk even more allergenic--the fascinating video "The Whole Truth About Milk" explains this process. All types of allergies are becoming more common now--but often they go unrecognized until they cause severe problems and are impossible to dismiss. Intolerances are often completely unrecognized because they are difficult to test for and doctors don't like what they can't test. But if you have tried everything and your child still doesn't sleep, try eliminating the common allergens and see if it helps.
***1 ounce protein per 2 pounds of weight for 12 month olds. So a 20 pound baby will need an average of 10 ounces of protein per day.