20-Year Prospect
We wish we could tell you that no one will need your job in the future...that everyone's brains will be healthy and stable and tumor-free forever and ever.
Unfortunately, that's not the case. First, there's the aging population, many of whom will require the support and medical care of a neurologist. Second, many of the diseases and disorders you're working with aren't going away any time soon. Just look at the incidence rates for brain cancer, which have been increasing for the last three decades (source).
It's depressing, but c'est la vie d'un neurologist.
On the bright side, you have job security. While the health industry is definitely undergoing some changes, and you may not make as much money in the future, you will definitely still have a job.