tough one.
I had a similar situation with one of my sites. Basically I was accidentally ranking for other terms that brought in good traffic on a daily basis. But I had no content for the visitors to enjoy and therefore they left.
One thing you could do is create an opt-in list for the more general traffic. Simply write a guide or create a sub-service that will be of use for these types of users and even if you only get a few signups per day, it will be better than nothing.
Alternatively you could put adsense on your site. When people can't find what they are looking for they sometimes click adverts just to leave the page. There are some highly paid ads for the medical terms.
Give me a shout if you need more help.
Dean