Mathematically, a natural monopoly sees its average cost decrease over all quantities of output because its marginal cost doesn't increase as the firm produces more output. Therefore, if marginal cost is always less than average cost, then average cost will always be decreasing.
A simple analogy to consider here is that of grade averages. If your first exam score is a 95 and each (marginal) score after that is lower, say 90, then your grade average is going to continue to decrease as you take more and more exams. Specifically, your grade average will get closer and closer to 90 but never quite get there. Similarly, a natural monopoly's average cost will approach its marginal cost as quantity gets very large but will never quite equal marginal cost.