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