I've never had a card acceptance problem on aircanada.com, but then again, I don't maintain credit card profiles online if I don't have to, and AC's website is no exception. I have no default credit card filed with them.
I memorize all my credit card and bank card information so that it's not much of a chore to re-enter the information manually each time I need to use it. You could say that the digital age has been good exercise for my memory!