20-Year Prospect
It's golf; we highly doubt the sport is going to become so unpopular that golf courses are turned into animal sanctuaries or anything like that. The sport has its own channel, a few magazines, and deals with broadcast and cable networks.
Though viewer engagement is rather low in younger audiences, it's probably nothing to worry about in the next twenty years. Like football and baseball, technology and graphics are bringing the game into the 21st century.
The PGA is worth over seventy billion dollars, and that kind of money doesn't just disappear overnight (source). If you've got the raw talent and can put the practice hours in, you can hang with this career all the way to the senior tours.