**Core Concept**
Intractable diarrhea in children can be caused by various gastrointestinal, infectious, or metabolic disorders. The primary issue is often related to malabsorption, excessive secretion, or motility disorders affecting the small intestine or large intestine.

**Why the Correct Answer is Right**
The most common causes of intractable diarrhea in children include celiac disease, which is an autoimmune reaction to gluten leading to villous atrophy and malabsorption. Other causes include bacterial overgrowth, such as in short bowel syndrome, and pancreatic insufficiency, which impairs the digestion and absorption of nutrients. Additionally, certain infections like giardiasis or cryptosporidiosis can also lead to prolonged diarrhea.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because it does not specify a cause of intractable diarrhea. A common cause of intractable diarrhea is lactose intolerance, which is not listed.
* **Option B:** This option is incorrect because it is a treatment for diarrhea, not a cause.
* **Option C:** This option is incorrect because it is a symptom of diarrhea, not a cause.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that celiac disease can mimic other conditions, such as Crohn's disease or ulcerative colitis, and must be ruled out in cases of intractable diarrhea. This can be done through serological tests and intestinal biopsy.

**Correct Answer: A.**