Yep, Doug, I'd say you were at the limit. Good thing you had enough fuel to allow eight approaches!
I had the fuel, but was running out of patience and energy. Once approaches and landings like that start going badly, things can start to snowball, and just like the wisdom of not trying to salvage a bad landing, it's often best to go some place else when something like that is going on.
The problem at the time was rapidly building convective activity and mountainous terrain. There was no where to go; other airfields were under the same conditions. Large thunderstorms were building in the heat of the day and I was returning from a fire that had been caused by lightening and was wind driven. I had no intention of going back out: I just wanted to get the airplane on the ground and tie it down. As the storms moved through that particular valley, the winds shifted to follow them.
In the same airplane at a different location, I experienced a hydraulic failure when the pump shaft sheared. I was returning to a small mountain airport to pick up a load of retardant, and upon arrival found that my three hydraulic pressure gauges were flat. The airstrip was narrow and relatively short, but the airplane's only form of steering was differential braking (largish, conventional gear airplane: turbine M18 Dromader). Without brakes, in that crosswind the airplane wouldn't have stayed on the ruwnay; it wouldn't have ended well. Also, without flaps, it would have happened at a higher speed, too.
I diverted to another airport where I recalled a good crosswind runway; as it turned out, that runway was no longer in use and overgrown (remembered it from a long time ago). Two other runways were available, but the one I needed was closed due to resurfacing and men and equipment on the runway. I needed it anyway, and requested it from a recently-installed tower. The tower ordered the men and equipment removed, and told me I could have the runway at my risk. Same scenario, lots of thunderstorms building, fewer and fewer choices time went on.
The only other option that day would have been a road, but that also would have put me away from crash rescue and other assistance. I already had an abnormal/emergency, and didn't want to compound it further. Fuel wasn't the issue in either case, but as things progress, especially after repeated attempts, one tends to become frustrated, and that can lead to mistakes or poor decision making. In most cases, it's best to cut losses, go somewhere else, get on the ground and re-evaluate. It's also best not to be in that situation to begin with, of course.