I think the answer is in the question really. Static websites fail because they are static, and never change unless it is someone’s job or responsibility to change them. So many times I visit a web site related to some project or other that I’m interested in, and feel like I’m probably the first person who has looked at the site for months, despite the fact that I’m fairly sure the project is still active.
That’s why I like WordPress a lot, and why I use it for my website. I’m now at a stage where all my online identities feed into WordPress and present a fairly unified view of what I’ve been doing, what I’m thinking and what I’m listening to. And most of it happens without me having to do a lot.
Yes, this took a while to set up, but most of that was experimentation. I could rebuild everything in about an hour now, and all it would take to make the site look current is the occasional bit of text typed in to one of the two firefox extensions I use for updating everything (ubiquity and deepest sender). I can update things on the fly, publish within seconds, and can also solicit responses from other people. All these make the site look like someone gives a damn, which is half the battle sometimes.
So yes, for all those people who maintain websites that were last updated years ago, it might be time to consider something more dynamic or even removing the site altogether. Especially if you want to attract new people to your project.