A car is a machine and can run for as long as it has gas in it without any issues.
You can drive your car continuously for as long as you can safely drive the car before needing a break.
Cars could run all day continuously if you could afford the gasoline and could drive it all day.
The human driver would need to rest well before the car would actually need a rest.
So drive as long as you can and don't worry about the car and as long as the temperature of the engine is staying cool enough and not getting too hot then it's okay to continue driving it.
The most I've been able to actually drive my car on a road trip is 2 hours before I had to get out and rest myself.
The car also got rest during that time but it probably didn't need it.
However I still needed gasoline and needed to check the engine oil as well.