Okay, the obvious answer is "the robots were programmed to keep the people alive" but hear me out here.
Buy N Large is a profit-making company. One of the central themes of the film is wasteful consumerism. The idea is that Buy N Large was so very driven by profit that they ignored the wider consequences of their actions. Yet the business is so successful that they are never held accountable for these consequences, and they eventually abandon the earth. Their customers are launched on-board huge space ships where robots take care of all of their needs, constantly feeding them entertainment.
It's also declared that the ship was only supposed to be gone for 6 years, but had just entered it's 700th anniversary.
Enough with the exposition, let's get down to economy. Buy N Large exists to make money, but there's no money being exchanged on the Axiom. Yes, I know that an answer to this question suggests there's a "pay later" option but that makes no sense.
People are born and die aboard the Axiom and never work. They have no way to contribute to the economy. They have an ever-increasing debt which they have no way to pay back, just an ever-increasing debt.
Buy N Large is a profit-making organisation, it's not in their interest to give every human being unlimited credit, and they clearly don't need any contribution from the human beings.
Just like if I walk into my local supermarket with no means to pay, they've got no reason to let me walk away with the goods. Wouldn't the Axiom robots stop serving the humans? Because they're robots, wouldn't they just wait, maintaining themselves, until some humans with currency arrive and need their services again?
Side note: The ship has abandoned it's mission to return the humans to earth, the Auto-pilot actively prevents this. So they've no reason to think that humans will ever contribute to their society again.