20-Year Prospect
One day, when technology has advanced enough to the point where our consciousnesses can be put into indestructible robot bodies (preferably ones with lasers), embalmers won't be needed. Until then, the circle of life will go on and end-of-life services will be in demand.
The thought of this job becoming automated someday seems pretty unlikely, as well. There are so many different duties that an embalmer is responsible for. Robots may eventually perform surgeries, but they probably won't be creatively styling someone's hair anytime soon.
Barring some radical change in our idea of how the dead should be honored, this job will be around as long as the bodies keep piling up. They say the only two sure things in life are death and taxes, so there will likely always be embalmers―and tax people, but you didn't go into accounting.