By speaking by strict rules, the shield bonus from Two-Weapons Defense should not be lost when flat-footed (as long as the character is wielding the two weapons), since shield bonuses are not lost when flat-footed; but I was wondering if this should be treated differently for two main reasons:
1) Weapons are not as large and covering as a shield (rather, they're usually pretty thin), which may offer some protection even when not readily set to parry an attack.
2) I tend see the purpose of the feat as using the two weapons to actively parry (by catching an enemy weapon in the crossblades of your swords or whatever, you get the idea) and thus wouldn't grant any shield bonus when the character is caught by surprise and the like.
Opinions? (Official ones, particularly.)
RAW, you should get the AC bonus when flatfooted. If someone strikes at you when you're flatfooted, you could argue that since you are sans Dex bonus, your reflexes aren't a factor. Do that, and you could argue that you deprive the target of the shield bonus. That leads to denying Reflex saves when flatfooted. Try to avoid it and just accept that the person still reflexively parries even if they're too slow to leap out of the way of an attack.
Holding two weapons doesn´t necessarily mean that you parry or even try to parry an incoming attack, i mean you get no such a thing as a parry attempt.
As is see the fact you are holding two weapons alone grants you the shield bonus, like holding a shield it makes it harder for an opponent to find an opening in your defense because the ways he is able to attack are limited - he can´t strike you the same way he could if you weren´t holding abything in your off hand.
So he should retain his shield-AC bonus from wielding two-weapons even flat-footed.