I don’t think there are any static sites on the internet. They are either growing and changing, or rotting away. Decay is a dynamic process, too. Sites need to be refreshed. I have a eleven-year-old blog (next month), and have found most of the links in the first couple of years have rotted away, and need attention. I need to update the underlying OS, web server, runtime language and site application. Vendors and the community provide updates and security patches.
If I visit a site and it’s in HTML 4.01 with marquees and animated GIFs of envelopes flying into mailboxes, I make some (pretty severe) judgments about the proprietors. If the owners hard-coded their names, addresses and contact info into all the pages, they will always, always miss one of them when they update.
So, while your content, organization and basic layout may not change THAT OFTEN, they’ll need changing, so why not use a dynamic engine that will make it easy?