the limit to let people spar before they step out
This is probably another reason to have one or more third parties observing. Not just heat exhaustion, but simple fatigue.
Unnecessary injuries can happen when you're tired. I received a broken finger (crushed) because my body was too tired to react on demand.
Being a martial art, it's entirely possible to happen when fresh even under the best of circumstances. However, I fully acknowledge reality in that situation. I was too tired and should have stepped out long before.
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One idea is to watch the clock and rotate people out. This will give a small breather, and force one back into the analysing mode for a moment as they observe the others.

