Final answer:
Prolonged sinusitis may persist despite antibiotic treatment if it is caused by a viral infection, fungal infection, or antibiotic-resistant bacteria, as antibiotics are only effective against bacterial infections.
Step-by-step explanation:
The most common cause of prolonged sinusitis that is not improving with antibiotics is often due to an infection caused by a virus, rather than by bacteria. Viral infections do not respond to antibiotics, as these drugs are designed to target bacterial pathogens only. Additionally, fungal infections or antibiotic-resistant bacterial strains can also cause sinusitis that does not improve with standard antibiotic treatment. In such cases, a different approach or medication may be necessary to treat the infection successfully.