The dog would most likely have a heat stroke and go down. Hopefully it will never happen that your bulldog would have to stay caught that long but if it happens then yes I would expect a catchdog to stay caught as long as his body would allow..
I saw where someone had posted they like a catchdog with some self preservation, well if a catchdog that I'm feeding cares anything about "self preservation" then he better CATCH when I turn him loose..
But what a man feed is totally up to him..

agreed....if you are using a gamebred pitbull, your dog should be able to last longer than 45 min, weather and temp. permitting, i dont think you should hunt under extreme conditions though, gamebred pit dog matches are known to have gone past the 4 hr mark, and this is against another gamedog, hogs are tuff too though, maybe an ear would come off, or the hog would go into shock, I hope no one has to find out this truth the hard way, but it will happen eventually unless youre careful.but even then, you never can tell
Just to add what you pointed out about game bred pits. They are culled hard on the stamina department and when they were fought they were in tip top condition and they were put on all kinds of supplements to stay in top working form.