One of the problems with Dogs and endurance is that they can't sweat. In order to cool themselves down they need to pant, evaporating water from their tongues. AFAIK, they are unable to pant while running and need to come to a stop.
Yeah that's what I thought. Humans are better endurance runners than dogs and horses, we can easily run further, speed up and slow down without expending too much energy can and can sweat while running through the heat of the day while animals must stop and pant. We can chase them down until they over heat and and collapse.
http://www.physorg.com/news95954919.htmlhttp://en.wikipedia.org/wiki/Persistence_huntingSounds cruel but we used to chase down sheep like that on our farm when I was a kid.