I'd say the +5 Defending shortsword keeps its hardness and hit points. This is because the magic of the blade, which is what makes it harder in the first place, has not diminished... merely shifted around.
What I'm trying to avoid, which the increase-to-AC-reduces-hardness/HP crowd's ruling would lead to, is a situation where a guy is fighting a sundering enemy and not making use of his sword's defending property. The enemy damages the sword quite a bit, but is killed. The next day, the defending-shortsword guy starts fighting again, and decides to transfer some enhancement bonus to AC. The sword snaps in half.
Or, on the brink of having his sword sundered, he drops it. And it becomes stronger again.
Those situations seems absurd to me, and worth avoiding. And so...
The bonus the defending sword gives to AC is unnamed, it just stacks with all others. The source of that unnamed bonus is a Weapon Special Property and an enhancement bonus. [Not RAW] So I don't have any problem saying that the bonus is an enhancement bonus that stacks with all others. [/Not RAW]
If you make that change, the sword retains a total +5 enhancement bonus, even if three of it is attack/damage, and two of it is AC. Similar to how you still have $20 wether its one twenty, two tens, a ten and two fives, etc. The sword keeps its HP and hardness, a Weapon Special Quality improves in the face of sundering, and magical swords don't break all of a sudden.
It might not be strictly RAW, but it's bloody well close enough.