I have been having this problem for like 2-3 weeks already. if you notice more carefully, there's a flash of a red error message saying that you should only enter alphanumeric for the account number or something - I don't understand why such error since certainly the account number is all alphanumeric. at first I saw there's this website update last week Nov 23 or so and thought it's going to address this, but no, still the same problem.
my workaround now: go to asiamiles.com to log in, once it's successfully logged in (and in the cookie or something), then go to cathaypacific.com, then you'd be logged on there successfully already.