Which maintenance task is NOT associated with improving energy efficiency?

Repairing leaky faucets is indeed not directly associated with improving energy efficiency in the context of HVAC and building maintenance. This task primarily concerns water conservation rather than energy efficiency. While fixing leaks is essential to conserving water, it does not have a significant impact on the energy consumption of heating, ventilation, and air conditioning systems.

In contrast, tasks like weatherproofing doors, checking air conditioning units, and cleaning the vents all relate to improving the efficiency of the energy systems within a building. Weatherproofing doors can prevent drafts, which helps maintain temperature and reduces the workload on heating and cooling systems. Checking air conditioning units ensures they operate at peak efficiency, while cleaning vents facilitates better airflow, contributing to overall energy savings. Therefore, repairing leaky faucets does not directly contribute to energy efficiency in HVAC contexts, making it the correct choice for this question.