Same exact issue trying to use Chase Reserve on Cathay Pacific India website. Stuck on VbV for a few seconds, then transaction denied. Even tried to do with a Chase rep on the phone. Still no go. The CX website would always return a message for me to contact my card issuing bank.
Eventually had to use Amex Plat.
Happened twice in April.
A lot of strongly worded secure messages to Chase finally got me a call back from a Chase supervisor that said basically it is CX's fault, which I know it's not.
This is something new that has started to come up. I have been using my Chase Reserve (earlier Sapphire) card to make similar purchases on the CX India website for several years (probably 20 completed purchases by now ranging from $3-4k USD).
Lesson learned. Amex is dependable. Visa/MC not so much. If I'm out of the country, I will not leave home without my Amex.