If it is a kitsune the three times could refer both to the number of requests it fulfilled/the amount of times the kitsune will take her form for its own amusement.
Since folklore about kitsune say they require that the kitsune place a leaf on its head, and it the manga on the last page we see the kitsune dropping leafs on our reluctant lady.
@exxp for the most part it showed that she been able to understand the language of the majority of spirts that she came across, with only the most beastly being