It might be a site that does not allow saved passwords. In Safari preferences (under Autofill I think), you can check a box that will allow these passwords to be saved, but the tradeoff is that you must install a lockscreen on your computer. I had the same issue arise when trying to log on to the American Airlines site.
I have not mastered all the details of iCloud Keychain yet. I'm hoping for a comprehensive article somewhere after the experts have had some time to play with it.