**Core Concept**
The child's recurrent sinopulmonary infections by bacteria with polysaccharide-rich capsules suggest a defect in the immune system's ability to recognize and respond to these encapsulated pathogens. This is a classic presentation of a problem with antibody-mediated immunity, specifically against polysaccharides.

**Why the Correct Answer is Right**
The correct answer is related to the immunoglobulin subclass responsible for recognizing and responding to polysaccharide antigens. **IgG2** is the subclass primarily involved in responding to polysaccharide antigens, particularly those found on encapsulated bacteria. This is because IgG2 antibodies are more effective at recognizing and neutralizing polysaccharide capsules than other immunoglobulin subclasses.

**Why Each Wrong Option is Incorrect**
* **Option A:** IgG1 is the most abundant subclass of IgG and is primarily involved in responding to protein antigens, not polysaccharides.
* **Option B:** IgM is also involved in responding to polysaccharides, but it is not the primary subclass responsible for long-term immunity against encapsulated bacteria.
* **Option D:** IgA is primarily involved in mucosal immunity and responding to protein antigens in the respiratory and gastrointestinal tracts.

**Clinical Pearl / High-Yield Fact**
A deficiency in IgG2 can lead to recurrent infections with encapsulated bacteria, such as Streptococcus pneumoniae, Haemophilus influenzae, and Neisseria meningitidis. This is an important consideration in patients with recurrent sinopulmonary infections, as early diagnosis and treatment can prevent serious complications.

**Correct Answer: C. IgG2**