Have they checked for Celiac disease?
Is he breast fed or bottle fed? He could have a food allergy or a food intolerance/sensitivity. Anything mom eats, he also gets, and if he's drinking soy formula, soy is a very, very common food intolerance.
It sounds like his body is unable to process or take out of the food what his body needs, so that his body is more or less "malnourished." A low BUN score will cause malnutrition because the body gets insufficient dietary protein (yet you state he had a lot of kidney work already done; does that include GFR and creainine tests?). There's also severe weight loss if a person has a magnesium deficiency.
Inborn Error of Metabolism (taken from Wikipedia):
I strongly urge the mother to visit this page of Wikipedia and look at the information it has on (Congenital) Metabolism problems. At the bottom of the page, there are six (6) different charts that categorize metabolic problems. THIS would be where I would look for clues.
Failure to Thrive (taken from Wikipedia):
The physiologic basis for failure to thrive (FTT) of any etiology is inadequate nutrition.
Growth failure is due to an acute or chronic disorder that interferes with nutrient intake, absorption, metabolism, or excretion or that increases energy requirements. Illness of any organ system can be a cause.
Most children with nonorganic FTT manifest growth failure before age 1 yr and many by age 6 mo. Weight is the most sensitive indicator of nutritional status. Testing: Extensive laboratory tests are usually nonproductive. If a thorough history or physical examination does not indicate a particular cause, most experts recommend limiting screening tests to a CBC with differential, an ESR, BUN or serum creatinine level, urinalysis (including ability to concentrate and acidify), urine culture, and examination of the stool for pH, reducing substances, odor, color, consistency, and fat content. Consider malabsorption conditions, such as coeliac disease. Depending on prevalence of specific disorders in the community, blood lead level, HIV, or TB testing may be warranted.
I pray there are able to discover what the little one has.