My own experience:
Had the same difficult experiences with "Verified by Visa" while trying to purchase airline tickets on an Asian carrier on several occasions. Had to call my credit card company repeatedly and, much the same as @Carolinian's experience, dealt with CSRs who could see no evidence of my trying to purchase the tickets. When they could, they were often unable to do anything about it. To me, it seemed like the back-end IT systems that handle the credit card transactions and the VbV authentication process weren't communicating properly.

I asked one CSR "Do you get complaint calls about "Verified by Visa" often?".

"All the time...", she said.

I think I finally just gave up and booked a flight with a different card on a competing airline. After going through this several times, I felt that I'd rather give up the money savings -- both on the ticket and on a foreign transaction fee -- if it meant that I could stop wasting valuable minutes of my life on hold for people who couldn't fix the problem anyways.

Credit card fraud is a real issue and I understand the need for airlines to rigorously authenticate users at the point-of-sale (especially if doing so gives them a better rate with the banks). As far as I can tell, however, the Verified by Visa program is poorly implemented. In my case, it drove my business to a different airline -- and to American Express instead of Visa.

I can't help but feel that I'm not alone in this and, if I were working in the IT/Finance departments of an airline, I would have real concerns that the incremental savings gained by using Verified by Visa in my checkout process are being offset by frustrated customers going elsewhere with their business.