The word that means the same as "not very often" is "infrequently". It can be used to describe something that happens rarely or at irregular intervals.
The word that often means "very often" or "frequently" is "repeatedly." It implies that something happens again and again, indicating a high frequency or recurrence.
Another word with a similar meaning to "not very often" is "rarely." It implies occurrences that happen with low frequency or only occasionally, rather than being commonplace or regular.