The spell in question:
Drawing upon the Plane of Shadow, you shape a quasi-real masterwork melee weapon of a type you are proficient with. You may use this weapon to make attacks as if it were a real weapon, dealing normal damage for a weapon of its type. The first time you hit a creature with the weapon, it may make a Will save to disbelieve; failure means the weapon deals damage normally, success means it only takes 1 point of damage from the weapon’s attacks. The weapon only deals 1 point of damage to objects.
If an attacked creature has spell resistance, you make a caster level check (1d20 + caster level) against that spell resistance the first time the shadow weapon strikes it. If the weapon is successfully resisted, the spell is dispelled. If not, the target may save to disbelieve as normal.
At 5th level, the weapon gains a +1 enhancement bonus. At 10th-level, you may increase the enhancement bonus to +2 or add the frost or keen weapon property. The frost and keen properties have no effect if the target makes its disbelief save.
The spell ends if the weapon leaves your possession.
It would make little sense to call out "the first time" if they got a save every time. I think it's basically one chance unless new information comes into play, the same way I would rule when a character interacts with any other illusion (otherwise, players would just keep poking the thing until they rolled a 20).