Why is once not an adverb?

The Word "once" is indeed an adverb. It means occurring on an occasion, or having occurred previously but not now.

*One construction to make the distinction is to place once after the verb if it means one occasion to date. Place once before the verb to indicate that it is no longer being done.

Example:

"We went there once" (one time)

"We once went there" (previously but no longer)