I believe I know the cause of the problem on the Renfe site because I recently attempted a purchase that failed, and I also run a site that sells Renfe train tickets, so I am familiar with the problems that can occur at the point of purchase.
Renfe seems to use the 3D Secure/Verified by Visa security measure for card payments (very sensible, because there is a lot of online fraud for online train bookings). When a "merchant" (in this case Renfe) integrates with a payment gateway they can choose to refuse or accept bookings on the basis of whether the customer passes the 3D Secure test. If the customer fails the test, then it is obviously a good idea to fail the transaction.
However, sometimes the card-issuing bank (or Visa/Mastercard, I'm not sure which) can choose to allow the customer to proceed without entering their password, because they have other ways of checking the payment is genuine. The requirement to enter a password is becoming less common. In this situation, the customer's payment should still be allowed to proceed, even if they haven't entered a password, because the bank (or Visa/Mastercard) has said it's OK (and they take responsibility for any fraud, should it occur).
What seems to be happening with Renfe, is that they are treating payments where the password has not been entered as the same as when the password has been entered incorrectly, and refusing all payments. They need to change it so they only reject payments where the customer is required to enter their password, but they get it wrong.
If you want to book trains tickets on my website loco2.com you are free to do so. Prices are the same as Renfe but converted into British Pounds (we hope to offer Euro pricing soon).