What is the evolutionary reason women have better muscle endurance?

Not all of that is entirely accurate. But the short answer is because the labor to deliver a baby takes longer than the acute burst of energy one needs to take down a woolly mammoth. 

Evolution doesn't work like this. There isn't a "selection" reason for every "trait" you can imagine. If these features exist, they're likely part of biological mechanics. E.g., women have stronger immune systems because of their ability to get pregnant. That effects recovery for diseases and endurance as a byproduct. They have different metabolism distribution and fat for fertility reasons.

People who lifts less weight will recover faster than someone who lifts more weight.   People who run slower recover faster than people who run faster, etc.  Women recover faster.

Women on average retain more body fat than men.  They don't shed this fat easier.  

The answer is you have bought into a false or at least misleading premise.  

Because the speed at which men recover and resist fatigue is more than sufficient to maximize their survival rate. They don't need more muscle endurance to survive. Women have to go through significant stresses in order to complete the childbirth cycle, and the fetus's health is tied directly to the mother's health during gestation. The more fatigued she is, the more stresses there are on the fetus.  

less muscle mass than men, makes women do all those things faster. women don't make as much ATP as men. 

There is only one study that came to that conclusion that put 9 women and 8 men against each other. No idea how such a tiny study proves anything. The research was done by the University of British Columbia for what that is worth. 

The funny thing is that feminist societies all over the west now promote that study and treat it as fact. Can you think of another study that involved so few people that is so widely respected? No? Yeah, I can't either. 

My answer is that the conclusion is feminist bullshit much like studies done by the left wing Harvard university that say women are better leaders.