Interesting piece of information.

When I created my 2nd BAEC account, I've used the exact same password as my other BAEC account.
Having the same login error made me think there's some piece of information that BA can't process right.

I've changed my password, NOT to include any special character (like #, !, +, *, ...), only plain letters and numbers.

This solved my issue.
(for now?)

It's also raising my eyebrow as the login details should be hashed on the device and never sent in plain directly to BA, even on https. That's a major security concern.