Answer:
Admitting to Thirst
Explanation:
Zeroni and Stanley were exhausted from the heat and, therefore, were dying of thirst in the dry hot desert! But, one of them didn't want to admit who was thirsty FIRST. I think of it as a who'll jinx first, but on a larger scale that wages on their survival, all for some pride! The pride of not being the one standing down, admitting defeat, they blame each other for who's fault is who's.
Enough of my yapping, the simple answer would be: Who will admit who's thirsty first.
Just a spoiler ahead, when they drank from that pond and went down the Hill, the curse was lifted and their luck turned from bad, to instantly good!