It lasts as long as the spell does unless the ability specifically specifies otherwise.
Some 3.X/PF abilities can be frustratingly vague when it comes to their wording, but for the most part you'll see things laid out in fairly clear black-and-white in cases like this. So, here, the ability is worded as follows:
"Change Shape (Su) A kitsune can assume the appearance of a specific single human form of the same sex. The kitsune always takes this specific form when she uses this ability. A kitsune in human form cannot use her bite attack, but gains a +10 racial bonus on Disguise checks made to appear human. Changing shape is a standard action. This ability otherwise functions as alter self, except that the kitsune does not adjust her ability scores."
Which means that indeed the Kitsune obeys the duration of the spell, since no other duration is given. However, this ability is Supernatural, rather than Spell-Like (though I can't imagine why - Paizo's mess, though, not mine), so UNLIKE Alter Self it cannot be dispelled, nor can it be counterspelled. It's still subject to antimagic fields.