The closest I've ever come to quitting in the middle of a round was my first time at Flyboy, during the ADGO event in November a couple of years ago. Heavy thunderstorms all night the night before, still going on that morning. Temps in the low 40s, winds at least 20 mph and gusting to 40 or so, torrential rain. Start delayed by a couple of hours. Started on the runway hole (18). Brand new golf umbrella blown out by the wind before we even started. By the time we made the turn back by the hangar, I was cold, drenched, and worn out mentally, and was seriously questioning whether it wouldn't be smarter to just settle in at the hangar and wait for all the other idiots to finish. At least one in our group did just that. But the rain had slackened a bit and the sky was getting lighter, so I talked myself into staying out. Several more strong downpours and four hours or so later, we finally finished. There wasn't a dry stitch on me, and it took two hours to even begin to warm up, but I made it. And the course was everything it was made out to be -- so much so that I'd do it again in the same conditions.
The most I've ever wanted to quit because of exhaustion was at the IDGC, in June 2010. It was a two-round, one-day tournament, with the Rec division playing Jackson in the morning and Steady Ed in the afternoon. Temps were in the mid-90s, and humidity was extremely high. Jackson took a lot out of me, but I didn't realize how much until about 6-7 holes into the afternoon round. Despite Steady Ed being shorter, by the ninth or tenth hole we played I was so tired and dehydrated that if it hadn't been nearly as long to walk back to the building without playing as it was to keep throwing, I'd probably have done so. I was drinking a half-liter or more of water at every cooler we hit, topping up the liter bottle again before leaving the tee area, and drinking all of that before we hit the next one. I was still throwing, but I quite literally did not care a bit about what happened with the throw -- I just wanted to be done. I actually didn't play all that badly for me -- about 40 points above my rating at the time, and 40 points better than my morning round at Jackson (Steady Ed being much more my kind of course), and I wouldn't hesitate to go back and play either or both courses (for one thing, I'm 70 pounds lighter than I was then) but I'd definitely want to do it under better conditions. I was able to compartmentalize my reactions to the courses (liked both a lot) from my physical reaction that day (no fun at all).
I still haven't played White Oak, just west of Atlanta, but those who have tell me it's quite a workout, with tons of dramatic elevation change. Richmond Hill was a lot of climbing up and down, but didn't absolutely destroy me or anything. Caddying for my son at Eastway during Worlds (fifth of six rounds in four days) was tiring and the sun was brutal at times, but not so bad that it kept me from going back out there the next afternoon after his morning round at Hornet's Nest and spending six hours shooting pictures, waiting out the lightning delay, and then spotting for the Advanced Women for the last several holes when it was too wet to take the camera back out. Still haven't made it to Renny, except for what I saw when we were at the park for the putting finals and what I've seen in pictures, but from that it looks like it would be tiring but manageable.