20-Year Prospect
Judaism has been around for over three thousand years (source), and as long as there are Jewish people, there will be rabbis. Funny how that works, right?
While employment for clergy is pretty steady across the board (source), rabbis are going to find more opportunities in parts of the country with larger Jewish populations. That's just common sense. You're not going to barge into an Amish barn and demand to perform a Seder. That would be weird.
While every other job is reeling in terror of automation, we can comfortably say that the chances of rabbis being replaced with robots have to be zero. Possibly some kind of negative figure. The point is that clergy might be the one field that will never have to deal with that sort of thing, at least until the First Reformed Church of Skynet gets its Terminator Priests up and running.
They say that a job in the clergy isn't a job or even a career. It's a calling. So, chances are, if you become a rabbi, you're going to be doing it for as long as you like. While the recession hit everybody hard (source), there's still a vibrant market for the services—the real, literal services—that you provide and you should have no problem finding a position (source).