While it wasn't a 24 hour race, I recently did the hells500 everesting epic and it took me a shade under 25 hours to complete. I had a similar breakdown and a good cry with about 6 laps of Stromlo to go (I was doing 54 reps of the road climb, it had been raining for 21 hours, it was 2.30am etc etc) and was glad that I had someone there riding with me or I could potentially have pulled the pin. I've had someone else who's done a few 24s tell me that "Half of 24 isn't 12, it's 18" and I think that's what you'd be feeling. Nice to have an actual answer to why it happens though!