my point is, can a human reasonably stay within viewing distance from a dog that is running away from him? the dog can just run at top speed, gain some distance, take a little rest and maintain that distance at a comfortable pace.

I used to believe in the endurance hunting thing until I realized playing with my dog it didn't make sense. They DO get tired, but they take a 1 minute break and it's like they are back square 0.

For the record, I'm in shape and with a pretty light frame (181cm/70kg) and go for 10km/1 hour jogs regularly.

On a steppe? I think so, I don't see why not. An animal running at or close to top speed might only speed up its exhaustion - it's much easier to run 1km at a steady pace than to do 10x100m intervals.

Try to play with your dog for an hour at high intensity. If your dog belongs to a large or very large breed it'll get tired much more quickly than you - assuming you're in somewhat good shape.

I'm not advocating in favor of endurance hunting, I'm only stating that we can out-endure some large-ish animals.

Pretty sure this guy can catch your dog even if your dog was on cocaine, remained focus, and had someone feeding it water periodically:

[1] https://www.irunfar.com/aleksandr-sorokin-smashes-24-hour-wo...

It's only fair to compare exceptional individual to an exceptional breed. According to Google Husky can run 240km in a day. Exceptional Husky might do much better. Average Husky will easily outrun most human runners.

Still, this is an exception to the rule - overall humans outperform almost all animals when it comes to endurance running.