The very first site I ever optimized was a simple, out of the box FrontPage web site for my wife's tutoring business. That web site hasn't been updated in about 8 years -- no new content, no changes to typical
SEO things like alt tags, page titles, headings, etc.
But a Google search for "NJ tutors" brings up her site in the #2 position to this very day. A search for "tutoring in NJ" brings her up at #1.
For exceedingly competitive search phrases things might be different. But for this site and those of most of my clients, fresh content isn't necessary to maintain excellent rankings.