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Does hardness work as damage reduction, reducing the damage taken by the object each time it is hit, or does it work as bonus hitpoints? I think it's the former, but I'm not sure.

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Your thought is correct. Per the hardness rules:

Each object has hardness—a number that represents how well it resists damage. When an object is damaged, subtract its hardness from the damage. Only damage in excess of its hardness is deducted from the object's hit points

So any time the object takes damage, subtracts its hardness first. This is similar to how damage reduction works.

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It would seem this isn't a perfect parallel to the real world. There are a lot of items that will smash more from later blows than early blows (for example, weakening the outer shell early, and large amounts of damage once the insides are exposed). If that detail were necessary, I would consider using two separate objects - one on the outside with a high toughness that yields a new object with lower toughness once it is destroyed. – corsiKa Jun 16 '14 at 19:45
Gaming is not intended to be "a perfect parallel to the real world"; just an effort to establish systems to reasonably (and without too much time or effort) adjudicate real (rather imaginary) conflict. When rules are too far from 'reasonable', they can detract from suspension of disbelief, but they can do the same when they are too cumbersome. – Wyrmwood Jun 16 '14 at 23:21

Yep, no matter how many times a Str 10 commoner attacks a castle wall with sling bullets, it still isn't going to fall over.

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