20-Year Prospect
There's no fountain of youth—not even Ponce de Leon thought so. Since there'll always be aging people in need of surgeries, there'll always be a need for surgical assistants. Just like older cars, older people need tune-ups and, sometimes, part replacements. Because of the cool technological advances that make surgery safer, more people in general may choose to have surgery to improve their quality of life.
That said, robots might become a mainstay in the OR before long. The robots currently used in surgery are rather large and imposing fellows. However, behind the doors of research labs, there's a lot of work going on to create microbots. These little guys, in theory, could be placed in a patient's body to gather information or to carry out medical procedures. Just think of the TV medical dramas that could come from such advancements.
Robots aren't going to replace surgeons. Unless they rise to the level of Tony Stark's Jarvis in The Avengers, they'll never be able to make split-second decisions or have a real heart-to-heart talk with a patient. However, robots will become more common in operating rooms, and that means you'll increase your value as a surgical assistant if you know how these mighty medical machines work.
Even so, that's likely more than twenty years out in the future. You'll be fine in this career...for now.