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As the others have said, as long as the machinery is in good operating condition, and not being run flat-out for said 24-hours, I think the human part of the equation would be the weak-link...
For the model A (given my personal experience with a tired-old 87,000 miles jalopy), my biggest concern would be oil consumption... my '28 can easily go through a qt in 100 miles if I'm pushing it at 50 mph...
I'm sure there must have been endurance runs with Model A's back in its day...
CannonBall Baker used to famous for all sorts of coast-to-coast speed and endurance runs back in the '20s and '30s... including one where he drove a car cross-country in reverse ( think the car might be been specially modified ? )...