This was addressed in the film's script (and novel). Over time, the Blight adapts to a species, then begins to destroy it. Luckily for humanity, the crop that seems hardiest is corn. In the years since Coop flew away, the Blight has begun attacking corn, taking about a third of the Tom's crop around twenty years later.
Then the stalks came apart like paper, the updraft shredding some into rising shards, others slumping and crumbling into glowing piles; then that illusion faded, too. Soon there would be no corn, no field. Only carbon and dust, inseparable in their lifelessness.
“We lost about a third this season,” Tom said. “But next year… I’m gonna start working Nelson’s fields. Should make it up.”
Murph wanted to shake him, to make him understand that it would never be “made up.” But what was the point?
“What happened to Nelson?” she asked.
The expression on his face suggested she probably didn’t want to know, so she didn’t press it.
Interstellar - Official novelisation
The implication seems to be that they're barely staying ahead of the Blight by reducing the world's population, by switching to a high-intensity agrarian economy, by breeding hardier and hardier strains (with the help of the sort of genetic engineering and selective breeding we see at NASA HQ) and yet they're still well on track to lose 100% of their crops, and by extension all plant life in less than fifty years.
For the record, he didn't say that the Blight would destroy the corn within a year, just at some undefined point in the medium future
“Blight,” the professor said. “Wheat seven years ago, okra this year. **Now there’s just corn.” **
Something about that stung a little. He was, after all, a farmer.