British Airways said the glitch is believed to have been caused by a "power supply issue" and there was no evidence of a cyber attack.
Terry Page, 28, had flown in to Heathrow's Terminal 5 from Texas said BA had lost his and "about 50" other passengers' luggage.
Speaking to the Telegraph, he said they were told that they were hoping they would have their luggage on Monday.
"It's affected so many people," he said. "Some 80-year-old lady was standing around waiting for announcements, et cetera - and she fell over."
He added: "We helped her up and she said 'I'm just so tired'".