The Honduras international was due to move to the JJB Stadium on a season-long loan from Deportivo Olimpia with a view to a permanent transfer.
But the Home Office knocked back his application for a work permit.
Manager Steve Bruce said: "We tried to appeal and it fell on deaf ears.
He's totally devastated. We'd got a figure of £1.8m agreed and unfortunately it's not going to happen."
There is no further right of appeal and the 23-year-old will now return to Honduras just a week after arriving in England.
The Latics boss explained that a player needs to play 75 per cent of competitive internationals to meet visa demands. Thomas, who has 16 full caps, had reached that figure but because he helped his team qualify for Beijing he fell under that marker - Olympic games do not count as competitive matches.
"We didn't get a work permit for a stupid reason," added Bruce.
"That was disappointing because I'd been over there, our general manager John Benson had been over there twice; we're bitterly disappointed and Hendry is gutted."