In the interest of follow-up, others with this problem will get quicker service by calling their credit-card provider as SBB only offers help via telephone.
For one of my credit cards, the purchase was blocked due to hyperactive "fraud protection". I had the block removed and was able to purchase.
In the time I spent unblocking, the price went up 20%. It would have been more helpful if SBB or their payment vendor has simply stated, "Your financial institution declined the payment." Then I would know where to go. I wouldn't wonder if it was the SBB website, the credit card processor, my bank, or simply what browser I was using.
All this does not explain the price rising and falling 20% during the many times a purchase was attempted; that's on SBB.
It also does not explain why verification from another credit card provider did not work and that transaction was blocked as well.