3.0: The change is permanent, until an additional use of the ability is used to change back.
The Alternate Form ability of the Hengeyokai (Oriental Adventures, p. 10) inherits most of its functionality from 3.0's Polymorph Other spell:
Hengeyokai can change shape, assuming one of three possible forms. This supernatural ability functions like the polymorph other spell...
Polymorph other (PhB, p. 236) has:
This means the effect lasts forever until dispelled. Since Alternate Form is a supernatural ability, it cannot be dispelled, so the effect simply lasts until the next time the hengeyokai chooses to use the ability again to change back.
This is also corroborated by the wording of the ability's uses per day, which implies needing to use the ability an additional time to change back (rather than simply waiting for it to expire):
...a hengeyokai can change form a number of times per day equal to 1 plus his character level. Thus, a 1st-level hengeyokai can switch from human form to animal form and back again in a single day.
Note that, contrary to part of the question, this means a first-level hengeyokai can use the ability twice per day (once to change, and once to change back).
3.5: Almost certainly the same, unless you're being an enormous RAW stickler.
Oriental Adventures received an official 3.5 update in Dragon Magazine #318, but the only changes to the Hengeyokai were to change their type from the deprecated shapechanger type into humanoids with the shapechanger subtype, and to remove their level adjustment, neither of which have any impact on Alternate Form.
However, the 3.0 polymorph other spell was removed in the 3.5 update. According to the official D&D 3.5 Accessory Update Booklet, its functionality is split into two successor spells, polymorph and baleful polymorph. Of these, only baleful polymorph has a permanent duration, while polymorph is arguably the better fit for the Alternate Form ability (since it's an ability that polymorphs yourself, not another).
Since the 3.5 update of Oriental Adventures makes no mention at all of the Alternate Form ability, my read is that its functionality should remain unchanged and use the 3.0 spell's permanent duration. However, I could see a particularly RAW literalist DM arguing that 3.5 spell changes would mean it now inherits polymorph's 1 round/level duration.