On small sites, a static CAPTCHA can provide some security against automated spambots that trawl e.g. Google for sites to attack.
Even though the CAPTCHA is fixed for each site, each site (hopefully) has a different one.
Basically, with a normal (dynamic) CAPTCHA, the payoff for solving it is the ability to make one post. With a static CAPTCHA, you get to make as many posts as you want on that site (at least until somebody notices), but you still need to solve a different CAPTCHA for each site. For small, low-ranked "long tail" sites, that payoff for a spammer may still not be worth the effort of spending a few seconds solving the CAPTCHA.
That said, if you're going to go that route, using an actual image CAPTCHA is probably overkill, and will unnecessary hurt the user experience. The same results can be achieved just as well just by e.g. asking your users to answer a simple question like "What is the name of this site?" or "What color is the sky on a clear day?", or even just "Please type 'friend' (not 'enemy') in the box below:".
This is not just theory: the MediaWiki QuestyCaptcha extension works like this. I use it on several small wikis I admin, and I've found it extremely efficient — so far, I haven't had a single spammer solve the (trivially simple) questions. (The fact that most of them are in a fairly obscure language may help.)