Thanks, Neil. I have now tried buying as a guest, but to no avail.
Yes, I figured as much when I tried to buy sale items (and failed). Now I've been attempting to buy a regular product; I wonder if it's a problem with CW's IT system or merely low stock of the watch in question.
Either way, I'm convinced that CW needs to improve its online store. I can't be alone in having difficulties trying to give money to CW – cash they should welcome!
Update: I finally spoke with Customer Services, and even they couldn’t take my money. While on the phone, their payment system crashed