20-Year Prospect
First, the good news: unless the zombie apocalypse comes ahead of schedule and America as we know it dissolves into an anarchic wasteland where packs of wild dogs roam the streets and small groups of humans jockey for territory with baseball bats, this career is safe.
As long as America has borders, those borders will need to be monitored to make sure that nothing nasty gets in. You could be sitting at that airport kiosk for decades, never once worrying that your career field could suddenly go up in smoke.
Now, the bad news: We have no idea what this job might look like in twenty years. We tried asking our Magic 8 Ball, but it just said, "Try again later." Like, twenty years later.
Immigration laws are complex and mutable. They're constantly being changed to adapt to the current sociopolitical climate. Who's in the White House, who's controlling the Senate, what kinds of wars and military operations the USA is involved in, the state of the economy, what American citizens are calling for, and what potential immigrants' home countries' situations are like—all of these intangibles affect the immigration laws.
And they can change in the blink of an eye. Remember how all the borders shut down after 9/11? We didn't want to let anybody in.
A mere decade ago, the trend was toward stiffening immigration laws to make it harder for people to move here. At the moment, lawmakers and citizens alike are fighting for immigration reform and promoting new laws that'll make the immigration process a bit easier for those seeking refuge in America. In the next ten years the pendulum could swing back, or it could keep going the same way. In twenty years—who knows?
However, no matter what the new laws look like, America will always need people at the borders and airports to make sure that the nation's safety isn't going to be compromised.
So, you're good.