**Core Concept**
Nephrotic syndrome is characterized by massive proteinuria, hypoalbuminemia, and edema. Children with nephrotic syndrome are at an increased risk of developing secondary infections, particularly peritonitis, due to their compromised immune status and potential for intestinal perforation.

**Why the Correct Answer is Right**
The most common cause of peritonitis in children with nephrotic syndrome is the translocation of bacteria from the gut lumen into the peritoneal cavity. This is often due to the use of corticosteroids, which can disrupt the intestinal barrier function. **Escherichia coli (E. coli)** is a common gut commensal that can translocate into the peritoneal cavity, leading to peritonitis. The virulence factors of E. coli, such as adhesins and invasins, enable it to colonize and infect the peritoneal cavity.

**Why Each Wrong Option is Incorrect**
**Option A:** Staphylococcus aureus is a common cause of peritonitis in adults, particularly those with ascites or peritoneal dialysis, but it is less common in children with nephrotic syndrome.

**Option B:** Klebsiella pneumoniae is a gram-negative rod that can cause peritonitis, but it is not the most common cause in children with nephrotic syndrome.

**Option C:** Pseudomonas aeruginosa is a gram-negative rod that can cause peritonitis, particularly in immunocompromised patients, but it is not the most common cause in children with nephrotic syndrome.

**Clinical Pearl / High-Yield Fact**
Children with nephrotic syndrome are at increased risk of developing secondary infections, particularly peritonitis, due to their compromised immune status and potential for intestinal perforation. Corticosteroids, commonly used to treat nephrotic syndrome, can further disrupt the intestinal barrier function, increasing the risk of bacterial translocation and peritonitis.

**Correct Answer: D. Escherichia coli.**